Learn Basic Algebra From Scratch | Mind Matters | Skillshare

Learn Basic Algebra From Scratch

Mind Matters, Solve Problems, Get Paid, Repeat

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34 Lessons (1h 57m)
    • 1. Introduction To Algebra

      5:17
    • 2. Algebraic Expression | What are they?

      5:31
    • 3. Algebraic Term | What are they?

      2:35
    • 4. Coefficients In Algebra | What are they?

      2:57
    • 5. Variables In Algebra | What are they?

      3:24
    • 6. PEMDAS or DMAS Algebra | What is it?

      5:28
    • 7. Like Terms | What are they?

      4:33
    • 8. Addition In Algebra

      4:42
    • 9. Subtraction In Algebra

      3:28
    • 10. Multiplication In Algebra

      4:38
    • 11. Division In Algebra

      2:57
    • 12. Factors in Algebra | What are they?

      3:02
    • 13. Value Of Variable | What is it?

      2:40
    • 14. Polynomials | What are they?

      2:42
    • 15. Monomials | What are they?

      1:37
    • 16. Binomials | What are they?

      1:34
    • 17. Trinomials | What are they?

      1:38
    • 18. Degree Of Polynomial

      2:43
    • 19. Names Of Degrees | What are they?

      3:10
    • 20. Indices Multiplication | 1st Identity | Basic Law Of Indices

      2:58
    • 21. Indices Division | 2nd Identity | Basic Law Of Indices

      2:59
    • 22. Indices Power | 3rd Identity | Basic Law Of Indices

      2:20
    • 23. Interesting Results From The Basic Indices Laws | Part 1

      3:18
    • 24. Interesting Results From The Basic Indices Laws | Part 2

      4:28
    • 25. Interesting Results From The Basic Indices Laws | Part 3

      3:18
    • 26. Interesting Results From The Basic Indices Laws | Part 4

      2:19
    • 27. Surds | What are they?

      2:50
    • 28. Surd Problems | Solved!

      4:29
    • 29. Exponential Functions | What Are They?

      3:55
    • 30. Graphing All The Exponential Functions | What do they look like?

      8:28
    • 31. Properties Of Exponential Functions | What Are They?

      2:31
    • 32. Absolute Value | What Is?

      2:13
    • 33. Absolute Value Properties | Part 1

      2:58
    • 34. Absolute Value Properties | Part 2

      3:07
13 students are watching this class

About This Class

Hi Students,

Solve the Assignment and Quizzes given in the pdf files. There will be additional tests and quizzes to test your understanding of this course. This is a beginner level mathematics course that discusses Algebra. You can consider this course to take you up to pre-university level ( You can sort of use this as a crash course for University Entrance Exams Preparation) or for those who have already studied this stuff and want a quick refresher with regards to the Basics of Algebra.

Transcripts

1. Introduction To Algebra: Hello and welcome back case. Right now, we're going to be here, actually, on the first lecture about a whole series about Elder brother were going to be discussing, okay. And just it is going to be the first radio about algebra Eso. I just want to go through the entire thing. That what? Actually, algebra is what you can do with her. Okay, on. Ah, what we're trying to do, we're starting algebra. Okay, So was actually started the ready right now. So the thing is that you have you have to think about algebra in terms off a puzzle. Okay, so this might sound crazy at first, but, um, you have to, like, believe me, this that actually does make sense or some substance are Please. It does look somewhat like a positive. We are the mindset that report inside off solving a puzzle. The way you try to solve the puzzle is the same. Um, the mindset that you need in terms of solving the equations on a on an algebra, uh, as a whole, you know, in general. So first of all, there's get out our example on. I'm going to explain what the equation about actually is trying to say, because this is not the start of the general way of writing equations. Hope. First of all, what is that? What this equation is actually telling us up? Is that what number can you add in to do so that you get the final answer out? As for Okay, so what is the number that you can are introduced so that you can get the answer for OK, I'll give you some time to think about this about this problem, and you can actually dispose the radio right now so you can actually think about it on, um, I'm assuming you did that on. So the answer turns out to be equal to do right, because when you are due into, do you get the answer for right So great. Good job. You solved literally. You just solve your first algebraic equation right now on. The thing is that a lot of people have already done this question before, but they're starting algebra right now. So what is this? That's what I should do. I'm just trying to, um I hope you understand. Now what you did overhead is that you actually dared saw at algebra equation. Let me rephrase the entire thing altogether. Okay, so it's actually say about your given an imaginary but Dr Given a box. Some boxes being average dude on. The answer is out equal to four. What is happening over here? Now, the thing is our what can you put inside that box? Okay, it's sort of a mystery, right? Like, what can you are inside the box so that you can get the answer out to be her before, right? So the thing is that you because this is like the seam. I actually just shortly the house right now. I shouldn't have done that. The thing is that the answer is going to be equal to do again because this is the same equation Dark report that a hard previously but you can see like the answer is out is out like air. It's truly right under the same, even though I hard like a blank statement and the 1st 1 and I have a box overhead in this one, what is happening over there? So the thing that that is happening is that actually what we're trying to do is replace a concept a a thing doctor, but it that is trying to represent a number. But that actually is not a number on replacing the are thing with the actual number. And in our previous case, this waas the box. Now it's an imaginary box. You'd normally actually Israel Bob's. There are no boxes inside of equations, right? So the thing is that we used our box, we use the concept off a box on, said Andi put the answer to insert the box. The reason being because the answer, uh, because regarding, like, it was blacks together because the box being added to do and the answer was born, if the number, it could be any number right. But in this specific area was do if the answer was different, we could have used some of the number 26 A. Depends on what we got out there so that the equation speaks up. Okay, so we were actually trying to link a box with a number two on that was what I was trying to do is trying to link a concept a something, something that is trying to represent something else. A number part is not actually the number itself. Right, So a number like do is something concrete. Like, for example, you have You can say that you have to fence. Right? So it is something like, Thank you. That is concrete. Okay, so that's basically what you do announced for all the time. And you have, like, successfully over here to solve two equations. You can say that. Either. Two equations. Could you like this is literally what you'll find in algebra. Like, uh, the answer is gonna be the same, but the questions might look really, really different. So you you have like, um Ah, this is great. Like you just saw do equations right now. So weapon to algebra. And that is all from my side for this specific radio on. I really, really, really hope you learned something you're watching. 2. Algebraic Expression | What are they?: Hello and welcome back. Ricky's. Right now we're going to be discussing algebra expressions, which is logically what we should be discussing right after we understand basically what algebra is. But again, let's actually get on with the pretty right now. But first of all, we need to understand something before our what people mostly do before moving on to algebra is called as, um ah scored as arithmetic. Okay. And what arithmetic is basically is is that you use numbers. OK, you solved, um, equation using those numbers. Okay, So, yes, I read medic. Not just a fancy name. This is basically doing a long time before before moving algebra, you say, like pupils do. Is it before or six plus six is equal to 12 or something like that arm. The thing is, our ultimate is actually pretty similar to this. Uh, so let's actually see what algebra has to bring us on out of the table. OK, so Oliver brings out as that it is actually a combination off using the numbers that you were previously studying on, it introduces something new, which is called out of the symbols. Okay, so it's actually introducing Assemble that you can use on our anyone can use. Um, let's say you use the black claim that I actually used in the first video. Or you can use the imaginary box. Are the normal box or something box a box? You can use the books or you can use letters. Are you can actually just use exclamation marks even because, like, these aren't actually real things. I'll on, uh, like all four of these. None of these aerial re just run. Um, well, the real things are numbers, okay? Those are the concrete things that we actually use inside of equations. But these thes symbols actually represent those numbers. Okay. Without it, the entire concept of algebra, those things are eventually all of the symbols are going to be replaced with the actual numbers. Our everything is our when most in most places of the world, people actually use the people use people prefer to use letters, for example, a veces x y z's and stuff like that. Any number, any off these any of the any of the letters? How many are there? 46 40 fighters. All of the letters. How maney No matter how many there are. Okay. So the reason actually for that is because it is convenient because most of the people who are starting that can actually. Right. Okay, So, like, basic English, they know the alphabets. Okay, so that is why I guess I'm not sure. But I guess now that is why people use those letters. And I think it might be easier instead of this growing boxes. Okay, so I do the actual main topic. Yeah. So the first example, this is the first set. First example. Do X plus y. Okay, so we're now we're going to break down, like, where are the numbers and the symbols, first of all, so this is going to be a example on example off the elephant also bring expression. Okay, So why worked out? Why would this be on a separate expression? Because it has the numbers over here, and it also has the symbols and assembled what had our X's and y's again? People use Lakers. The off of the the letters off the English alphabet. Okay, so, um, so it's over there. We were using Xers and wise over here on the other thing. Is the operations ever using now? Um, is addition, you can you can convert it into a subtraction, Okay? There's gonna be multiplication or this can actually even be a division. Okay, All of the four basic operations you are, subtract, multiply and divide. Okay, so right now we're using the additional one on. This is basically what an algebraic expression is on us to make things even more. Player. Let's actually go through some more examples. Okay? So, as you can see, we have the X y plus four on the screen right now. And over here, the numbers. That's actually, uh, you try to do this together. Okay, so let's first of all, try to figure out where the numbers are. Okay, Number two tell you where the numbers are. Three I'm before. Both of these are numbers on excess, and wise are the Are the repairs are the symbols okay on the operation over there is the addition one. Similarly, we have another algebraic expression. Why lost the see if you again. You can. You don't have to be restricted towards X is unwise. Um, you can use these. You can use a these or any off the alphabets. Okay. So, again, this is another example, off an AL an algebraic expression C plus squared of D plus five. Okay, again, you don't need to have, like, an individual like numbers. Um, the equation of the other Bring expression can have three parts like we have overhead or it can even have How many parts are there? 1234 We have four parts. And this out of expression that I just walk out onto the screen on what this house expression is saying Is that a squared lost under Macy? Because you see Cube plus five. So that is all from my sight. Uhm on these air basically what other expressions are So thank you for watching hand. I really, really hope you learn something. 3. Algebraic Term | What are they?: Hello and welcome that case right now we're going to discussing algebraic terms. Okay. In continuation. With what? With what we were discussing previously. Which was how the free expression. So this is gonna be the third video. Okay, so let's actually get into this on a stakeout. Our sample example out. And let's say you're given the for weighing thing in front of you. You were actually I last way. Now, the first thing, if you actually want is for if you want the previous video, you should know by now that this is what is called as an algebraic expression. Okay, this is what is hold as another expression as a whole. Okay, That is why I have underlying the entire equation now. But what about the individual terms? What are they going? In fact, we have two of these rooms being added together on it Turns out that these are actually cord as algebraic terms, and this is what we're going to be. This what we wanted to know. Like, what are algebraic terms? So the our first algebraic colonel, what is going to be two x y now? That is the first outbreak term and the 2nd 1 over there is the why, Okay, there's just a single. Why on that is our second LD break. Terrible That so? Basically what We are crying. What we're doing over there is that there are multiple algebraic terms. And when you have a certain combination off them, you are left with what is called as another to bring expression. Okay, so, yeah, you are left with or discourse us on algebraic expression. Now, let's actually try to understand it by using English. Okay, The language. English. So let's break it down in the former. Wait. Seriously, you're given a normal sentence like I like cops. Okay, So the words the English with words of what? Here are high. Like cats. These are three individual words on something similar is happening over there and mathematics that we have multiple. We have another big expression. Okay, so that's say we're just taking the previous example. Which Why, Aditya? Why, Andi? Unusual terms over here are two x y. And why? So this is like the germs combined together to make an expression just and like, in the same way as words combined together to form a sentence. Okay, so the algebra expression is basically the sentence on the algebraic terms overhead are just the individual words. OK, so that is all there is do outbreak terms. I really hope you learned something on Thank you for watching. 4. Coefficients In Algebra | What are they?: Hello and welcome that, Gates. Right now we are discussing coefficients on this is going to be us just breaking down Outbreak. First of all, we broke down all the big expressions down into algebraic terms on then we are going to be breaking down algebraic terms into their individual components. On one of those components are the coefficients. Okay, so let's actually get straight into the our example. Okay? That I was bring out something. So let's there, given the glowing thing in part of you do X Y on. If you actually want the biggest radio you are going to remember, not This is actually what is called as the algebraic term. OK, but what about this individual number that you see? Oh, actually, just story where that thing is, but let's say you don't know that. So what is that thing that I've underlying? A with screen. What is our? I thought you might see that this is a number. Okay. And you will be absolutely right about that too. Isn't socked in number? You'd be. But you know what? What do is right now in this position, it is a number, but other than dark, you know it's the coefficient over here. Off this algebraic terms on basically what you need to do to find out the coefficients off any algebra term is just look, act where the number is okay to the wear, whatever the number is. Okay, I'm not talking about the powers or anything else. I'm just talking about these individual numbers, if you can find it. If you can find that out, you have found your corporations. So yeah, that is all there is to coefficients on. So where were we? Actually, and this radio? Let's go through some examples, okay. And, um, try to go along with me. Okay? So let's say you given the farming thing to be X Y what is the coefficient over here? The composite video. Okay, so the answer is three. Okay? Place. Okay, let's take out another thing. 5 80 What do you think the coefficient is over? Where do you see the number of it? If you say five, then that is the correct answer. Okay, 75. Where do you think the number is now? It's not seven and 5 75 is, in fact, the correct answer over because, um, 75 is, in fact, one number. We know we're not going to say there are do coefficients over there. 75 No, we're just going to say they're 75 is, in fact, go officially. But our co efficient coefficients are like war. One algebraic term. There's going to be one coefficient. Okay, They're gonna be multiple variables, but we're not talking about that right now. Coefficients are always one. You can always have one coefficient often. I was a great car. Let's move on to do Why X square? What do you think is the algebraic karma? But it if you say, do a lot of correct There's all from my side. Thank you. Watching on. I really hope you learned something. 5. Variables In Algebra | What are they?: Hello and welcome back, guys. Right now we're going to discuss saying the other side of the equation, um is going to be the variables. Okay, now, what we were trying to do is basically dissect the algebraic terms down into their, like, basic components. We've already looked at coefficient, so now let's actually go through the vertical portion off it. Okay, so let's get our algebraic terms out on you given the following Think right part of you do Z. Okay, now. Oh, let's actually trying to find the valuable of it. And what do you think? Is this the variable? If you remember correctly in the previously we talked about this on this is in fact, northerly variable. This is what you call out? Deco Fisher. Okay, now what about the other portion Z as this d viable? In fact, yes. This is, in fact, of our on If you look at the term variable, it GIs basically news that something is changing. Something varies okay, on the word even variable means or something is very okay. So there's something Is the value off the off the term it can change. It doesn't need to stay a single number it and change. Okay, Now, let's actually look at another example in which we are going to, um In fact, find something out. There doesn't need to be a need to have only one variable president. We could have multiple variables. Bar. Um I remind you that there can only be one go fishing present inside off. Um, and I was a great curve, OK, they could only be one coefficient, but there can be multiple variables overhead on what do you think? How many are there over it? Um, in fact, but let me actually just tell you before this how we can actually find out. Ah, variables is that first of all, this located the coefficient. We is going to be any number not talking about the squid. Now we're talking about squares or powers of it, which is Lord, the normal numbers and everything else is going to be part of the variables and overhead. Okay, over there, we have do off the variables present on one of them is X, and the other is why. Ok, so both of these are letters, okay? Yeah, aren't they? Are the two variables present? So Donna searches this easy to find out. Um fired a difference between variable coefficient and even the differences between the individual variables of it. Now, to make everything solid, we need to go through some examples. Right? Example of is nice. Now you say you're given the following thing 58 What do you think is the variable of it? Yes. A is in fact, a variable. Let's try another 17 and then what do you think? First of all, how many variables for our president? But it if you said do and you are correct. But which of these are the variables? M and n nice? Okay, so Oh my God. So let's move on to 89 VCD as agency Really big algebraic curves. It's huge. Now what? What do you think? How many variables? Air President With it. On my never mind, you would only be one confession. So there aren't two coefficients eight and nine. There aren't two coefficients of what have been its only one go official 89 out of one Go ovation. Everything else is the very book I now see How many variables are president with it? Five. Okay, we have the see the s and a so yeah, that is all for my side. And you were watching on I really, really hope you learned something. 6. PEMDAS or DMAS Algebra | What is it?: Hello and welcome back. OK, so we're going to be discussing over there in this lecture e m the A s or in some parts, the world. This is called after the mass. True. Okay. On the bare bones of all of these, both of these and multiple other stuff that people like have is how do you in fact? So what is the order in which you are trying to solve an algebraic expression? Okay, there's all there is to the to this room. Okay, But it's actually just break it down. He m d a s. Now, if the first letter e it stars, actually for the word Prentice's. OK, so these are what are corner of the brackets, All the different types of records. All of these are discouraged from the all of these are just called print disease. Okay, now, these are going to be the first thing. They're just all when you are dealing with algebraic expressions on anything else in general. OK? Now, the next thing is the exponents part. Now the exponents, the e court, the E star's forward, the exploded and the exporters are all the powers. For example, we have a variable over a squared. OK, so that to the power, what is the exploding? And that is the next thing that you're going to be solving the M moving on the actually started swore multiplication on that is the third thing that you're going to solving on modification can written in different ways. You, some people, you the crosses or the hysterics are a simple dot OK, they're affordable ways off writing multiplication. But in fact, this is like the third thing that you're going to solve it going on. The sounds for division This is discount Peter. In what ways? These are doing all the ways you can write division on. This is the fourth thing that you go to solving a again starts for addition on, um similarly, as is as stunted subtraction on, there's only I guess there's only one way over 80 subtraction and addition. So, um, that that's what way. That's really sure over there. Okay, so now let's actually go and look out an example. Okay, so let's see. Let's say you're given the following example. Are you want to actually solve it? Using the actual rule on when you follow the rule, you get the correct answer when you don't follow the rules. Sometimes you actually get the wrong answers on. And that is why they ordered the rule is actually established. People follow the rules. No. The first thing that you need to do is the deep portion, which is the parentheses. And over here, you can see that there are two things that you need to be solving right away. Okay, First of all, you got to be solving the entity. Whatever is inside of the perhaps he's already solving our on the second course. Okay, so the next thing that you're going to be doing is solving the exporter inside of the parentheses again, inside of the parentheses, not outside. So will that solve Three squared and three squared is equal tonight. Okay, so now that we have solved C squared learners move onto the M portion and the M is In fact , if you remember a multiplication on, in fact, we find modification or on the first bracket, two times five. So that's after you've solved are two times five is equal, then have saw that moving on. We have the are in fact, the first bracket is completed we don't have anything else doing way. We don't have any other like operation being performed inside then So let's just remove the brackets. First pot now going on. Um, is there any division going on over there? And Ah, in fact, no. Any addition inside of the brackets again, we're looking inside the brackets. Reversible again? No, we don't have any addition, One of our subtraction that Oh, yes, we do have to traction nine subtracted or 999 When this work that just gives us fight on we we can get her to the brackets again because we are done with, um, or down with water operation. There wasn't. Now there's just a single number of runners we get to the brackets and we are left with 10 plus five Negative three. Now, we were over in desperation. Weaken Just randomly do all of the operations over there, but on it won't make a difference, But sometimes it does on. So we're again good. Following the rule on unlike Ford are when you do again, start from the very beginning, which is the B portion. Now we look at the P and there actually isn't any Bradley print disease over there. So we ignore that. Any exponents? No northerly. There aren't any exponents over. What about multiplication? And again, that's a no No division again. What? We do have a nation. Okay, we do have the additions or then added a five. That is, we're going to perform first default. Are we do that, then our defy That gives us a 15. And now we are left with the S and 15 negative. Three. That gives us, um wow. I actually forgot 15 military that gives us a 12. Almost screwed are going on. Okay, so now we have the actual answer. Where with the, uh, not a strong. Okay. And that is, in fact, the answer. And this is how you perform? Um, that's how you solve equations and solve admitting stuff. Like like we did right now using the rule. Okay, So similarly, you're going to be solving algebra equations. Um, overhead on. This is all there is to the rule. Thank you. Washing. And I really, really hope you learned something 7. Like Terms | What are they?: Hello and welcome back today. We're going to be discussing like, terms on because there's something that comes up in large when you are studying algae. Russell. Let's try to find out where they are on how to identify whether work we're seeing are like terms are are there unlike. Okay, so there's a car example out on. Let's say you're given the forming to algebraic, um, algebraic terms. Okay, so 10 maybe and five, baby. Now we're going to find out if they're like germs or not. Right now, I'm just going to tell whether or not these are like rooms. Oh, or not. And then we're going to discussing How exactly was there that I was able to find out the answer? Okay, so these are, in fact, like terms. And as you can see, that they don't exactly look exactly the same because one of them has the corporation 10 and the other house fight. But I'm going to still say that these are in fact, like terms are now. If you make a slight change, for example, in the five maybe algebra term, we're going to be making the B into a B squared are not makes it. And unlike term now, how exactly was that? I was able to find out whether or not these were like terms or not on four that happening to understand basic things. What are variables on what are their powers? For a first of all, variables are the letters okay, the A's and the B's and all of their taxi and the exponents are the powers activity are above the of other variables. So, for example, we have a these X's and y's for our variable portion on before the powers one we are. We like we have the numbers that written above those Pacific letters. Okay, the letters are the rightful. So the powers aren't in this specific case that the coefficients really do not matter. So you have to skip them. You have to ignore them on now. Other than doctor, you just have to see whether or nor the, um, the powers much on the variables, Matt. And if that is the case, then you have what are called the Spectrum's out of. That is not the case than that. And then then then you're just going to say that those are unlike terms. It's actually apply on and on an actual example. Okay, so just bring out something. Okay, So let's say we have the following do other returns to a be on for a B. Now, the first thing that we're going to do is identify the variables. Okay, Now, in this case, we have the ease. President, why don't we have the these present? Okay, that's good. We were done with the first part. Now we just need to see whether or nor the powers that be have are equal in art. Okay, so the exporters and use races are won. These are, in fact, again ratio of our one. So remember the exponents, Um, the experience matter, but the co visions don't. Okay, again, we are going to be calling this as lecturers. Okay? These are inside going to be like terms, because the coefficients on the because the coefficients on marker, even if they're different but over the valuables on there under specific powers were equal . So these are in fact, would be a called us like hers. Now, moving on to the second example, they were given the following to algebraic curves. Five a square D and then 80 square over here. We're going to be first of all. Okay? Where is the actual thing? I didn't always remember. Coefficients do not matter. And everything else doesn't matter. So even though we can see that the coefficients are different because they were just going to be ignoring them because they do not affect whether or nor the terms are like or not. Okay, So the first thing that the variables are in fact, as you can see, we have the A's present on. We also have to these presidents. So the variables we're gonna variable sport. But what about the exponents? A is squared and the first algebraic term. And the 2nd 1 the A raise raised to the power one. Okay, so there are different because of that. Are we're just going to be saying that these are unlike terms? Okay, you don't need to check the, uh because, like, you don't really need to check the at this point. But even if you do, uh, these are just going to be called as unlike curbs. Okay, So even these let's actually checked the bees out. Okay? And as you can see, the visa, in fact, also different and the first algebraic term. The B is Richard. Borrow one while in the second algebraic from the bees raised to the power to it is the square and find out is why they are different. They're all from my side. Thank you for watching. I really hope you learn something. 8. Addition In Algebra: Hello and welcome back. Today we are going to be discussing Algebraic Edition. OK, so first of all, let's let me go through, um, on actual example. First of all on let's say I'm given the following question. Do way out of four of the six say now the way that I would go about doing this is that I know that do A and six, they can be together. And so we are them on. I get the final answer 88 hour before, and now I can see that I can't really go any further because it is like the simplified form until there's going to be our answer. So how were how was it that I was able to solve this question? So let's go through the steps now. The first step is that we have to identify the terms out of the like. I previously had three hour break terms, right so out of these three hours a break terms, which are the term that can actually be outta together. A lot of the first up aren't to identify those from. The first thing that you have to do is find out those terms which have the common variables on similarly the common exporters variables with similar experience on. So let's bring out the exact question that I previously will strip soft away out of the 468 In this question, do A on six a are the two terms that have a similar variable with a similar exponents, which is a racial bar one. Okay. And as you can see in both cases in the way we have here is part one on in six A. We have a ratio of our one. So this is the thing that is common to go to them. Uh, so the next thing is is, in fact, trying to do the addition arm dark is to just Art Deco officials like, because they are to earn four, um, two and six times. You have to add them together and leave everything else. Okay, I'm a Z. You can remember I didn't touch the A race for one portion. I just added the coefficients together. OK, so let's do this. There are other through the second step right now. So this was what I previously hard do. A on six days work, I can act together. These are the terms that are gonna have together on now there's Arctic officials to get closer. To add it to six. That is an eight, right? So we are left with the answer 88 hours before on now we can't are 88 before because they are different. A a and eight and the algebraic ERM eight a. We have heiresses bar one on four does not have a variable. Pride decides it. So this is why we are would be are done with the previous question. So let's actually bring out another example. So, um, let's say you're giving the following question. This previous bout is actually quite long. Who a squared out of a added up to the attic before a squared out of 38. Now let's actually do the first step, which is to find out which are the terms are actually gonna actually be at it together. OK, so four doc those and that the terms are a square A aren't. Then we have three, which is like individually, Um, it was just a constant, and it doesn't have a very progressive, so the a squared terms. As you can see, I have, like highlighted them are doing squared and 40 square. So these are the terms are going out of the can be out together. Other than that, we have the smart one portion in this equation. The leader, the dukedom that can be together again because these are a units for one that is one a on that is three a. Okay, on we have three, which is, um, which doesn't have a partners or we're just going to be leaving three alone. Okay, so the second step is to in fact, at the D pairs together. OK, so let's actually are these do they got to? Yeah, that's are these two together? So do after four. That gives us a six on. You are just going to write six a squared, OK? No, don't don't like, don't do anything with the x squared. Just write a six a square. Okay, So good. So the next part is to rd one a and e three a together. Okay, so one a added three a What is one out of three? That is, in fact, 1/4 4 Right. So you're just going to write at the end for a You are not going to be touching the apron. Our anyone ever for a So as you can see six x squared after 403 we can't really, um, find out any other way to our this specific thing. Because, like, all of the variables are different variables where they're like, the variables with your power are right now different. We have a squared areas of our one and no variable. So we are, in fact, done with the specific question. OK, so that is all this tradition. Thank you for watching on. I really, really hope you learned something. 9. Subtraction In Algebra: Hello. And welcome back today we were discussing subtraction and how it is that you go about doing that in algebra. Um, on. So let's actually get straight into this. So there's going to be really similar to what we did in the previous video, which was, like, addition. Okay, which is really similar, but there are a few differences. So I'm going to show you how it is that I will go about doing this specific question so that some of the walking equation negative for a negative to negative to the that. The first thing I want to see is that negative four and negative three account. We subtract together. So, um, I just, uh practical, efficient together. Negative for native T. That gives me a negative seven eight of 78. That is the final thing. So negative seven a negatively was what I'm left with because there is nothing that Aiken do further do with a specific question. So that is why would you say that I would be done for this question? Are so this is going to be my final answer now. What were the steps in love again? They were there going to be do steps involved when you're trying to do subtraction to the first her The first step is that you have to find out the like terms. You have to find out the like terms, and those are the terms that you are going to. These are cracking together just like you did when we were trying to do it. Issue okay, Until the light comes air. Those terms, which have similar variables on those similar variables, have similar powers to them. Okay, so those are what are called as, like, terms. So again. So now the second step is that you just have to take those the like drums coefficients. Okay, on I'm so you just have to subtract them to get okay. So for example, we have the evolving equation right in front of us. So negative to a square. Negative three. A negative for a squared negative. 58 Okay, so, again, finding out the like drums is our first house on over. You can see that negative way squared. Atnegative, forte squared are the two terms that are like terms. Okay. I remember in, like, terms you don't have to care about the coefficients. I'm not taking that into account. All I'm saying is not a square in a square. H Burgess President, both of them. That is why they are called as Lakers. Okay, So, um Okay, so the next two terms that see if you can find any other terms over there, which are, like, on Okay, so we have two eyes. Did these a practice first? So negative to negative forces Step two. Okay. The step two was, sir practically coefficients together. Negative to negative for that gives us a negative six. Okay. Okay. So the next, uh, the next pair that I see is this technical three year negative 58 on the these Oregon like drums because both of these have a bridge too far. One in the on again. I'm ignoring the coefficients on the coefficients over here are, like, three and negative five. So the second task is to just surprised them together. So negative three. Um, negative three. Sepracor's five. That is just equal. Do later. Okay, so we are left with negative seven a square Aren't a negative 88 now because negative seven a squared is not a negative 70 square and negative. Eight a are not like terms. That is why we're just going to say that this is the final answer. Okay, that is all there is to subtraction in algebra. Thank you. Were watching on I really, really hope you learned something. 10. Multiplication In Algebra: Hello and welcome back. Okay, so we have already discussed addition and subtraction when it comes to algebra. So let's just move on toward application, OK? So first of all, let's bring out on actual example. Over there are like, so you're given the following equation A replied with two plus eight. Okay, so the brackets overrepresented are a is being multiplier with boat two on eight individually. Okay, so the thing is that a over there is being replied with a aren't along the dark. It is also being more replied, but do Okay, so the thing is that first of all, we're going to be more deploying a with a so a multiply with a that gives us and a square. Because how they have the same powers we were discussing that shortly on. Then a multiplied do That gives us a just to eight. So that is the answer. The way plus a square on because we can't actually simplify it any further. We are going to, um, redone with this question out of this is going to get the answer. Okay. So how was it that I was able to solve this question so either two steps in wall on. The first thing is that you whenever you see similar variables, you're just going to be adding the powers together. OK, so let's say you're given the following thing a multiplied with a Now both of these are similar where the full of these air variables on they have on their similar right. Both of them are A's. So the thing is that you just have to, um, are the powers together so 18 years apart, one multiplied with a racial part wants. So the answer is one out of the one that gives us a to so the answer is a squared. Okay, So the second step is that when you have variable which are not the same, are they or are they are like coefficients are being one of lard by the variable. You just put both of them together as a single term. Okay, so we're doing mean by that. So a being what of lie Bour do that just gives us to eight. Okay, Because these are not similar. The the answer over there is doing on if you are given the former yokozuna, just start doing some examples over there, so x multiplied with why, over there we can see that both of these air variables, but they are different from each other. So the answer is just going to be X. Why you just put both of them together, Okay? Okay. So on to our second example over here, you can see that both of these air valuables okay, both of these RVs on they are. Yes, similar. So you just have to are the powers together so bi racial are one. And the rays of the marijuana use is like our our powers together. So the risk the power want those one. So that gives us a B squared. OK, that's going to be the answer onto our third example. So this is actually ah, a combination of what we were starting previously. So let's just try to do this. So too much is being multiplied with with h r. Four B, and eventually you're going to be multiplying them. So there's first of all, motor play to age with H. So we have to age being multiplied with H. So h is both of these ages are going to be because they're similar. You're just going to be adding the powers together. OK, so h resto bar one and eight years apart one after, um, in our answer, that is just going to be hh first power do eight square. But because do was tagging along on it is it is are similar to h we're just going to be writing Didn t do along with the eight square. Okay, so this is going to be the answer off this off this term. We also way we are still Ah, we're still required to multiply to agent for V. So this is what we're going to be doing right now, And at the end, we are going to be writing the finances. So for this, you need to multiply both of these things separately. Okay, so two on four are going to multiply together on H and V a good who would like together, and then you're going to be combining both of these together. We're having about that Sochi confortable alleges would like to win for two times for that gives us an it. Okay, so, um other than that h times be just gives us hb right, because there are similar eso just you. So all you have to do is just put both of these together. So HB is the answer now wanted by eight with age beat. Okay, so when you do that, you just get it. H meat. The final answer is you get to algebraic terms on the first term is do it. Square on the other is positive. Eight HB. Okay, so this is the answer that this is all there is multiplication and algebra. Thank you. Watching on I really, really hope you learned something. 11. Division In Algebra: Hello and welcome back. Okay, so let's start out with division now, because we're not all multiplication. So doesn't just go through a division now. Okay, so first of all, let's just bring out our example. First of all, our little you're given evolving Question nine X squared. Why? This is like one singular term is being divided by three X z. Okay, so another way you can write. Ah, the revolving equation is this way. Nine x squared y divided by three eggs. Eat. Now both of these are similar, and I actually prefer the one that is written down below because it makes a lot more sense to me. Actually, when we're trying to solve the what, we're trying to solve the equation. OK, so the first step in war is you have to first of our divide the coefficients together in the first house breaker. We have deco fresher nine. And the 2nd 1 we have three. So you're just going to be dividing both of these together? So nine divided by t. That just gives us a normal answer, like three. Okay, So obviously, this is where we're going to be putting the answer. Okay, So brick by brick. We're going to be joining the answer together in In between. Okay, so three is the first thing that we get. Okay, So the second step is you have to find out the common variables. Okay, on you have to surprise the powers together off the common variables. Now, the order in which you do that actually matters. Okay, So X squared because X squared is the first term over there on the X eyes. The extras about one is the second girl. Okay, So you what you have to do is subtract the first terms. Um, it the first terms power comes first. Okay, On second terms, power comes second thing is what? I mean, do subtract with one. I'm not going to be writing one minus two because I was going to be wrong. Um, the crack way is to minus one, because X rays power two X squared comes first. X risk for one come second. So do minus one. That just gives us a normal answer. One on the answer. The actual answer. Doctor, Go to be writing his x ray Shikhar one. Okay, Now, Vitre step is that you have to leave everything else like the variables which are not common among the to algebraic terms alone. Okay, so you don't have custom. So in this case, we have wise. And why in the first room on we have a Z in the second algebraic. ERM okay, so we're just going to be leaving them together and notice not the easy does not come along with the three X y Okay, it comes down because z was in the second house of record on the second house. Your rectum naturally just comes down. Okay, so that is why three x y divided by Z, is going to be our final answer. That this is going to be our friend. That's OK. So that is all there is to division. Hang your washing. And I really, really hope you learned something. 12. Factors in Algebra | What are they?: Hello, and welcome back. Today we are going to be discussing factors when it comes to algebra. Okay, so But first of all, just for a quick reminder of what factors were, Richard is going to take out a example from arithmetic. Okay, so let's say you're given the following number six. Now, the factors of six are going to be three. Do. If you remember, this is what we used to call a fop. Agree on the reason. Ah, that three and to our call as factors of six is because three times two is equal to six. Or you can say that two times for using with six. So in that case, two and three are factors on. So let's hear them on the number eight on for eight. The factors are going to be four and two because four times two is equal to eight. Or you can say that two times four is a great step two and four are the factors. Okay, so in algebra, something similar happens. Okay, so first of all, we need to solve a question, and then you can actually get through the Actually, actually, actual thing that we wanted to discuss, which was Parker's. Okay, so that you were given the farming question five baby is being multiplied with 38 bluster. Now, how it is, doctor, go to be solving this question. Now again, five baby is being multiplied individually with three a on five. Evie is being replied. We're too are. So first of all to solve this question, you need to multiply 5 80 with 38 on you individually. So let's just solve the question for small 5 81 black with three. Okay, so five times three. First of all, we're just going to move into playing the coefficients together to fight a mystery that gives us a 15 on. Now we go on to find variables which are similar to vote of these. So a racecar one or just a normally. So both of these have every super one. So they just are the powers together. So a a squared is the answer on V. Just tags along because there's nothing to multiply it with. So 15 a squared B is the final answer. Now we're done with the first part. So if I may be multiplied with do is our next I think that we need to solve 5 may be modified to. So again, this looked actually pretty easy to do because Albany Tree is for supply five. And do the coefficients on a profession with the constant on were down five times. Do that. Gives us a 10 on 80 just types alone because we can't do anything else with them. So the navy. Well, the final answer is 15. A squared B attitude down a B. Now, what we have over here is going to be guard as an algebraic expression. On what we hard previously the two terms five a B on three A plus two. These are called as factors off 15 a squared B plus 10 navy. Okay, so, um, using similar notation as we use previously are in the factory. This is what we get because 5 80 multiplied with three. A plus two gives us 15 a squared B best and to be OK, so Oh, you actually get what I was trying to convey over there. Okay, So you're watching on I really, really hope you learned something 13. Value Of Variable | What is it?: Hello, and welcome back today, we're going to be discussing how it is that you go about solving questions and with the values of the variables has already been given to you. Okay, So usually what happens is that you don't know the answer to the variables you don't know. The values of the variables are This is how you're going about, um, solving these questions. Ah, that you, for example. They don't know the answer off these four variables. And while solving you get to know the answers off all of these individually and when you're done, you know the answer of all of these. Okay, So usually what happens in these cases is that another brick expression is given to you on , um, you want to find out the values of the individual variables. Okay, So again, a small note overhead is that let's say you're given you want to find out the Valley off do variables in that gays do algebraic expressions are going to be given to you, okay. And that is the only way you can find out the values off the individual variables. But the question that we're going to be discussing today are slightly different. In that case, you're given the answers, the values off the variables on your just door to simplify the expression, the algebraic expression. Okay, so what you actually mean by that? So let's say let's actually go about solving questions like these. So 78 plus four B is equal to question mark. All they're asking you is if you give you the values off a Andi, can you find out toward the out of expression? Um, the answer to leave algebra expression is can you simplify the other expression? So that's a year. They give you the answers, the values of the variables. So they they say that a little one on B is a country. So the first thing that you need to do is use substitute the variables with the values. So just in sort of a or the value one on it sort of v just court the value three. And now all you have to do is do simplify. You have to simplify the question on, um, you're going to be getting the answer out. So seven times one that is equal to seven on four times three. That is just equal to 12 right? So seven attitude 12. That gives us the answer. 19 on So what we have done over there is that the we have just simple fired the out of expression after we were told that these are the values of the individual variables. Present arms 19 is actually just include 70 plus four b where the values off a are one on the value of V is equal three. So that is all there is to solving questions like these. So when you were watching on, I really, really hope you learn something. 14. Polynomials | What are they?: Hello and welcome back. Today we are going to be discussing boy no meals on four that the first thing that you need to know is what are algebraic terms. I'm so far they are We are going to be taking the help of arithmetic. Aren't if you remember, and arithmetic. All we do is that we do you with numbers. Normal numbers aren't we Do certain operations on them. Okay, so these individual numbers are coral as individual terms that arthritic Okay, so do as a number 26 is a number seven is also a number are so these are individual numbers also, which can be called as unusual terms. OK, so, similarly, in algebra, we have something called As on the Great term. So we have to a negative b y que onda so on and so forth. So these are going to be the individual terms and algebra are. In fact, all of these algebraic terms are going to be representing our numbers. Okay, so two, according representing the the number 66 negative V could be representing the number seven like you'd night. Okay, So what will you know? Meals are are just a, um are just like a combination off these individual terms. Okay, so the minimum amount of firms that you need are two are so you can have, like, tree, but minimum do. Okay, so we're gonna have three or four or five. Er, how many, Um, how many want? Okay, so the bare minimum is that you need to have at least two. Okay, So inside of the other expression, Yes. So, um, for example, I just tried to make some algebraic terms over there. So, um, we're going to be making something which has do as a great terms. Okay, so let's say the first term is do a arm. The second term is three. I just made out a two way into a two weeks where so I just say the first almost away square on the second term was just a normal, constant three. So this is going to be another expression. Also, he put in over it. Okay, so our second example is going to have three algebraic terms, So let's say the first arms to 82nd drum is negative. A on deterred term as 97 y squared on the reason why I said that you just have to are The terms together is, for example, the middle one that you see, the middle outbreak term negative eight accuracy over there has a negative inside, but the thing is that the positive just makes way for that negative. So it just becomes to a B negative. A plus out of tonight sound y squared. So this is going to be our Well, okay, elevated. OK, so that is all there is to pull normals. Just a combination off algebraic terms. Just there needs to be a certain minimum amount. So that is all there is to other programs are by no means so Thank you for watching. And I really, really hope you learned something. 15. Monomials | What are they?: Hello, and welcome back. Today we are going to be discussing Bono mules of what they are, but they're not on. This is going to be in continuation off working previously discussed before boarding on those. Okay, but But again, like first fall, we just need to get a quick refresher about what algebraic terms are. I'm so on the screen you can see for algebraic terms, Okay? Even gets called the terms in simple words. So the first term is a which is just a variable. So the second term is for which is just a constant for a is just a combination of both of these are a Q is going to be a variable rates of the power three. Okay, So if you remember point no meals work. Those algebraic expressions, which hard more than, um, retired more than one algebraic term outer together. Okay, so the minimum amount was to on the upper limit. Could go as high as you want. So those were what we called for No means on. So what about out of expressions which only have a single German? Them. So these are going to be called asthma. No meals. Okay, so on the screen. You can actually say that to a X is going to be a mono meal on X y squared. It can also be called us a moment on the four algebraic terms or the terms that you saw previously are all of those individually can be called as more no means okay on If you look into the word more Romeo in a little detail, the word mono is actually a Greek word, which means single our individual. So that is one way off trying to remember or differentiate between Paulino meals on more novels. OK, so that is all there is to know meals you're watching on. I really, really hope you know something. 16. Binomials | What are they?: Hello and welcome back. We discussed mono meals. Let's just get into by no means. OK, so first of all, again, a quick refresher off. What algebraic terms were arms on the screen. You can see three algebraic terms do x three and negative b Y squared. All of these individually are going to be caught us outbreak terms or to simply just turns . Okay, so if remember, point no meals were, um a everywhere an algebraic expression which had a combination off at least two algebraic terms in the Okay. So the upper side could be as high as you want, but what about expression, which only has specifically to terms on? In fact, there's a name for that other expression, which is on the bike home. Okay, so remember, boy normals needed to have at least two terms in them. OK, But that was not like the end off the, um off, you know. Okay. The upper side couldn't be high as high as 25 or something. Okay? So binomial specifically only have to algebraic terms in them, which are added together. Okay, so let's say that the first term is to actually the second term is be cute now in total to extras, B Cube is going to be called as a binomial. Okay, so if you look closely into the word binomial, the word by okay is actually a Latin word, which means to on the word via also used a lot in the word bicycle earned by school. If you remember, has two tires. OK, so that is how you can remember our differentiate between Binomial is and Melo Meal on point omens. Okay, so that is all there is to buy Domino's. Thank you watching on I really, really hope you learned something. 17. Trinomials | What are they?: hello and welcome back because we have already discussed Binomial. So we're just going to move on to tie normals now and again. Just a quick refresher of output. Algebraic terms. Words were on the screen. You can see three algebraic terms. Why is a, uh, other baker do as another term five A. V Q in total 5 80 cube as a single term. Okay, so if you remember, point normal for those out of expression which hard? At least two terms being added together. So, um, a minimum amount that you needed were two on the upper cycle. Be as high as you want, but find about another algebraic expression. Were specifically has three terms. Now that expression as of course, going to be able No, no, but it also has another special name for it, which is binomial on. Um, Dino MEOWS cannot have two terms or four terms or more than that. It is specifically needs to have three algebraic terms. So let's try to make it binomial right now. So do X is going to be the first term. The second term is going to be seven and the third is the square. So in total to a X plus seven plus B squared is going to be a try. No, me. Okay on if you look closely, the word cry is actually a combination off Latin and Greek, which means the word in English. It means the word three. Okay, on, um, the word is actually used quite large. You know, bicycle is used a lot on, uh does one way You're trying to remember what Kaino meals are in Trying to differentiate them between from like, binomial more normal and Quinault meals is that nationals have three tires, right? So binomial also have three outbreak terms. Are you watching on? I really, really hope you learned something. 18. Degree Of Polynomial: Hello, and welcome back Today, we're going to be discussing the degrees. All the poor normals are you encounter in algebra on how it is that you could identify where the degree is. OK, so first of all, let's just get our simple example out under tell you given the following equation to a Q plus four for a squared negative seven on you want to find a word? The degree of the specific question is, Are polynomial is okay, so the first step to do that is do first. Well, just locate the individual terms on. Then you go and find out the specific term which has ah, whose variable has the highest power in them. Okay, so again, we have the following equation right in front of us. 90 squared plus four BQ. Plus why so, First of all, just locate the terms. We have three terms of her hair. 90 square or be cubed on wireless Too far. One. So these are the individual terms present and out of these, the one with the highest power is for Vic. You okay? Are so we're going to say that this algebraic expression or point Romeo has the is off degree three. Okay, so again, back to our original example to wake you Plus for a squared negative seven. Now, for the first thing is that how many terms or President with him? There are three terms present on which, uh, term has the highest power. And I was going to be a Q. Okay, so do a Q has the highest power present. So what is the degree going to be? It is going to be degree three. Okay, so this algebraic expression is on Gregory three. Or you can say that this polynomial is off degree three. Okay, so now on to something slightly different. Well, like how? How are you going to solve this specific question? If you look into this Ah, algebraic expression or polynomial? You see that there is the first outbreak term is a squared B Q. Now, this is going to be slightly tricky. So what do you actually do is whatever you're given such an algebraic term, you just are the powers together. OK, so a first of all that how many ultimate terms president? OK, so we have three years great terms, president. On the the actual thing that I wanted to go to was that you have Are the powers together cigarettes are the powers off Do off A and B together. So do. Plus, retard isn't going to be able to five. So this outbreak term has the power five. Okay, on the next algebraic term B squared house, if our do on the next term for a years, for one has the power one present. Okay, so Ah, these are the three powers president. And out of these, the highest power is off a squared B cube. Okay. And so this is going to be called as a degree five equation. OK, so thank you for watching on. I really, really hope you learned something. 19. Names Of Degrees | What are they?: Hello and welcome back. We have already discussed. How does that you go about finding where the degree of an equation is? So let's just go through or the different names are. OK, so we've already discussed. How hard is it to go about finding the degree off a specific equation? So, for example, we have the former equation right in part of us a squared plus three meat. So the first thing you see is, Doctor, the term a squared has the highest power to okay. In this case, I'm so that is why we're going to be calling this a degree, prove term. But instead of just calling this indignity to term of these terms, the equations which, for example, a degree to equation, they also have specific names for them, which we're going to be discussing. So, for example, degree two terms can be called us quadratic equations on. So let's just go through the list one by one. Okay, So the determines which, um, have the powers arranged power zero. And that is the highest power. You're just calling them constants. Okay, So for example, we have 758 All these normal numbers is that these are just going to be called out sponsors . So if you have, um, a term which have the highest power one that is going to be called as a linear term. Okay, So for example, we have a plus two in this case. So to logistic constant, while a is a variable which has the highest power one in this case. Okay, so that's why um we're going to be calling, not a linear equation. OK, so terms, which have the highest power to those record as quadratic equations, we just went through one of them previously. So this is another example a squared plus a plus do. And as you can see, that the determine a squared has the highest power do in this case. So that is why this is a degree to term on. We can also be calling this a quadratic equation. Okay, so, degree, three terms equations are called Ask you big versions. Okay, So this is an example off a cubic equation. A cube negative. A square post seven. So the term a cube has the highest power three in this case, and that is why we go to be calling this a different future are just ah cubic equation. So similarly we have. If the equation that you have is have the highest before that I was going to call it as a Kordic equation on this is not a good example. Okay, so I just say that the first room to a cube instead of to a Q. We hard the determined to a mission of our four. In that case, this would have been a quart equation. OK, okay. So moving on with the 5th 1 Ah, that's what we call as equity equation. If there is a term say, for example, we have evolving a question and part of us do a reasonable five negative a Q plus A square foot seven. This has the term. The first room to a December 5 has the highest power five. The variable A has the highest bar five in this case on That is the reason why we're going to be calling this a degree Pfeiffer or just a critic term. So you basically don't need to go further than the cubic equation, but I covered I still cover do more a questions just like for clarity's sake. So how does the whole from my side thank you for washing and I really, really hope you learned something 20. Indices Multiplication | 1st Identity | Basic Law Of Indices: Hello and welcome back. We have not moved onto starting Indus is on in the specific video lecture. We're just going to be discussing how it is that you go about doing multiplication when it comes when it says so. This is sometimes called as the first identity on the equations, three types of equations that we're going to be solving our ass shown on the screen so you can see why. Cube Times wire issued of our five. So what? What is the answer? That's the That's the question everybody itself on. We're going to be going back to the question, but first of all, just need to understand the property, and it's actually quite simple. It may look daunting at first, but it's actually really easy, so just go through it step by step. So the first property actually, states start. We have some number A. We just raised the power, and some number are that is all of that is multiplied with again the same number A, which is again raising to some different power em. Okay, so what is going to be the answer? And the property actually tells us where the answer is going to be. But first of all, I just make it somewhat easier for us by actually giving them some real numbers. Um, the specific values. So let's just just give that. So let's say that the value off a history, okay, this is going to be our base on. Let's say that the value off and is going to be five on the value of m is going to be able to do so. What does the equation become? This is the final equation that we have on the bar. Okay, three races are five times to religious power to. So basically what the first property states is that if you have something similar to what you see on the screen, what you are, what you just have to do is to just are the powers together. Have, um, in this case, just treat written in the bottom as the base. So the answer actually becomes three. Initiative our five out a trip to on. So this actually gives us 500 do that? Gives us a seven. Okay, So the answer becomes three races of our seven. Okay. Started all the rest do the first property. So if you actually go back to the question that we saw, Like, um, in the starting. That was why I Q I'm wires are fire. So all you have to do waas, right? Why I as the base on have ah, three out of the five. Cigar gives us 5678 So why rest of our eight? So that was the answer. Okay, So what? There's only Ah, there is actually a warning. There is a precaution that you have to take when you are applying this rule, which is that the bases need to be same. Okay, by again, just a quick reminder of what I mean by bases. Is that number that I wrote three. Okay, are the variable that I do Notre docked with, which was a Okay, so it all you have to ah, take care of that boat. The things that you're multiplying have the same basis. OK, so there's all from my side. Thank you for watching on. I really, really hope you learned something 21. Indices Division | 2nd Identity | Basic Law Of Indices: Hello and welcome back. We have not move around a division after multiplication on. So this actually sometimes called as the second identity off witnesses on the type of question, everything we solving are shown on the screen. So eight of our end developed being divided by a receipt of RM. So what is going to be the answers? This is the problem that we're trying to solve today. Armed. So let's actually go through the the second property. Okay, so the second property actually says they are, um when a we have a number A Okay, which is raising the power end being divided by the same number. A race to a different power m OK, so these are the specific types of questions on which the second property hordes Okay, out again. A quick reminder because I think this is really important. Ah, the value of a Gandhi. Any number that you want. OK, it could be it could be for 378 whatever number you want, but the But the important thing is that a needs to be a okay. You can't have seven rich about and being divided by six rated power em and then apply the second property over there. You can do that. So let's say you have the number. Let's take the body of a seven. So the value of a we decided that it was seven. So value of a is going to be seven in the first term on also in the second term of Gray said that the thing just become seven reasonable and being divided by seven races rm. Okay, so this is what it comes, aren't on Lee And this just a specific case, it does the second property horse. So don't go about using the property on any other equation, OK, so to actually make it a little bit easier for us to understand the second property there just give the values give the powers actual value. So let's say the value of energy with sex like em is equal to four. Now. The second property says that all you have to do is subtract the powers are important the base again. We don't touch the base. So the base actually just comes out as it s so Ah, the answer. Do this specific question is going to be a know it totally some base. We're going to give some number to devalue A. Okay, so we have six in this case on. Then we have four. I'm just subtract six with four and you get the answer to Okay, so let's give Let's say that the value of a is actually seven. So seven Richard votes Ah, 70 Sparber six being divided by seven Gracia par four. The answer over here again is going to be just seven because seven walls of vases seven reached up over you because six minus or gives us the answer to so seven squared is just equal to seven times seven. So that gives us the final answer equal to 49. Okay, so there's all there is to division on the second identity or fitness is so thank you for watching on. I really, really hope you learn something. 22. Indices Power | 3rd Identity | Basic Law Of Indices: Hello and welcome back. We are now moving on to discussing how it is there to go about dealing with powers when it comes, tremendous is on. So this is sometimes called as the third identity on the questions diaper trying to solve our has shown on the screen. So what do you do when you have something? Um, some question right in front of you. So something similar to what you see on the street. So what the question says is nine is racial power. Six are all that is being ah, square. So how do you actually solve these questions? Okay, so we're actually going to be solving this specific question, But first of all, ledges go through the specific property. So the third property actually just says that if you have some number A, which is the base in this case which is raising up our end at all of that is being racially , our M and other power. All you do is that you multiply the powers together on you have the base again. Um, we don't touch the basis, so the base remains the same. So all you do any times m just means and is being more deployed with em. All you do is multiplied the powers together. Okay? All you have to do it justly, like literally what all all you have to do. So to make it out, to make it easier for us to understand that just give the deep hours actual value. So I just say that value of and is even three on the value of em is equal to four. So this is what the question becomes. A list of our three are all of the operations Power for all you have to do is multiply three with four on the answered it then becomes prov. Right? So a region of our 12 artist e while answer that is all the rest of their property. Okay, so we're back on the question that we left from in the beginning. So nine Richard of over six on all of that is being square. How do you go about solving this question again? We multiply the powers together. Six is more going to multiply. What do on the answer off? This is going to be equal to 12 right? So six times two is in recall. So that is going to be again. That that's the power. But what about the base? We don't like the bases. So nine again. Nine discomfort out there. Naturally. Okay, so that is all there is to third property that you're watching. I really, really hope you learned something. 23. Interesting Results From The Basic Indices Laws | Part 1: Hello and welcome back. We have already discussed three basic laws, and now we're going to be using them to get some interesting results out. Okay, so the first thing that I wanted to discuss was, as you can see on the screen, we have already gone through how to solve questions similar to North you see, on the screen, which is a Q being divided by a relationship. Or if I, Bart would actually just going to be solving this again to get something really interesting at the end. Okay, So if you remember correctly, well, you have to do to solve questions similar to so what you see on the screen is performative subtraction. Okay, So the way you surprise is by taking the first power, the first variables power with stream. This case on use of Procter did with the second variables power. Okay, just five. So three negative fire that gives us the final answer equal to negative two on. So the base. That's good for, like, the power. But what about the base? And if you remember correctly, we don't past the base. The base remains the same. So it was a before, and it's going to be a in the answer as well. Okay, so another way of writing division, instead of just using the slash, is by using the symbol RTC on the screen on yet another way of writing division is by, like, making it into a fraction. A cube becomes the new miniature on a visit bar five becomes the denominator. And now we're going to be using this Pacific way of writing equations, Um, for to actually get some useful stuff out. Okay? First, all this specific question in a slightly different way. Okay, So a cube, as you can see on the screen right now, eight, you can also were done in the following way. A mortified by a multiplied by eight on. We tried not in the new manager, because artist how you write fractions. Okay, on, uh, and the bottom, you can see that our daughter's areas of our fire, right. So it is a par five is basically just saying that a is being multiplied with itself five times. Also, a multiplied by a live A multiplied by one multiplied by again. Okay, um, so now what have to do as you actually simplify the equation? you can view that on the way you can do that is by cutting out bears that you see in the numerator and the denominator. Okay, so what I'm actually saying is every if you see an A in the upper side in the numerator, you can cut it out if you cart one a out in the denominator ASB OK, you can cut both of these out. So I like, I I heard the first pair out on Beacon. Similarly, we can cut the second pair out on dirt there out. And what you're left with is one in the new miniature on you, ese and the Newman and in the denominator. Okay, so one over a squared, Yeah, there's going to be equal to one over a squared are. So if you actually, uh, they close and look at it one way scored is actually just equal to a risk. The power negative too. Okay, so we get equal results even if we don't use the, um of, like, the rules we started previously. Okay, if even if you don't do that, we can just use normal logic. You come to around, sir? Okay, so we get that you said we have got the same results. Okay, So that it was all from my side. I thank you for watching, and I really, really hope you learn something. 24. Interesting Results From The Basic Indices Laws | Part 2: Hello and welcome back. So this is going to be our part. Do off using the basic laws to get do some interesting results. Okay, so there's actually get our example out. And if you remember correctly, we were actually doing this before. Hard. So a cube divide by a cube. You can solve this question by just performing a simple suppression on the way you do that is, you pick up the first power, which is to in this case, are you subscribe docked with second power, which is again three in this case. Okay, so three negative three are gives us the final answer equal zero Nagar. We have the power out. Okay with zero. But what about the base? And if remember correctly, we don't pass the base. We had a before on. We are going to have a in the answer as well. Okay, So air is the power zero is going to be our final answer on directly get do the resort. We have to perform another that we really you're just going to be solving the same question again, using the second room matter that we discussed previously. So we have a being multiplied with itself three times. Okay, so am I. But I am glad I e Okay, then we have the same thing in the denominator. And if you remember correctly, we can just solve this question by cutting out beers from from the human. It, er Anna on from the genomic. Okay, so what are Yeah, that is what we're going to be doing. So let's actually do that regard the first pair out the second on Also the third pair are, and what we're left with are the is going to be one divided by one, which is going to lead us to the final answer, which is equal to one. So we have the final answer equal one. So what we actually just found out is that we saw the same question, but God, different results Or actually, that is what it may seem like at first. But in fact, any number raised our zero is actually just equal to one. This is a group with edited it like this is proven on. We have already Well, actually just proved out ourselves right in this pretty OK, so it doesn't have to be a ritual bar zero the any number braces. Barbara, zero is just going to give us the answer equal to one. Okay, so this is This is actually the result of that. I really wanted to show you guys. Okay, So our second thing that I really wanted to discuss was how do you make a or any number risk for one? Okay, you can use the first property that we discussed on the first. Nobody asks. You just says, are you? If you want to make, um, some number of our one, all you have to do is are two numbers which can give you the answer one. What will you do again? Uh, do just, like, have what we're discussing. Clearly that, uh, we have the answer overhead. Okay, areas of our one is going to be an answer. And they were just trying to construct the question right now. So this is what we have. A reserve are ones where the answer on we have two numbers, which we are waiting too hard to actually. Just get the answer one on. You can do that by having 0.510 point five. Right. So was your bun fight added a 0.5 can actually give you the answer One and you don't have to be restricted to one. By do you can use any number. But I issues Europe on five in this case. Okay, so what about if you want to make a risk for one using three different using using three numbers. Okay, so we have heirs of our one by do multiplied by air is about one by two or what? What if you have another heiress, the power something. How do you make one in doctors on You can just do that again. This is something normal Kardashian practice stuff that we're doing right now. So one by three, we can use the number one my treat one, but really actually just equal to in decimal form as he will disturb 133333 and just keeps on going. But if you really want to concise number, you just use one like three. So one night Riyadh one by 3 to 1 by three. I was going to give us the answer. Avery Sarwan. OK, you can just, like, continue on and on. If you have four numbers, you can just use one by four out of the one by four out of the one by for added to one. My four. OK, so yes. So right before we end this this specific topic after we're discussing, I just want to, like, give you a small, um, it small yet off. No. Okay, So areas where one might do is actually just equal Who? Uh, the square root of faith. Okay, so I just wanted to have that over here because this is actually going to be used in the future videos. Okay, So thank you for watching hand. I really, really hope you learn something. 25. Interesting Results From The Basic Indices Laws | Part 3: Hello and welcome back. This is the third part off us getting some really interesting reserves using three basic laws that we have already studied. Okay, on the thing that I want to be discussing this specifically lecture is how do you write a number for you have same number Everest A car and over em. How do you write it In the second form, which is in the root form. Okay. Aren't we actually do this is by having let's say you have and as the numerator as you can see on the screen. So what do you do is you ride the end, which is the numerator inside of the route right next to the A OK, on you, right. The denominator, which is the M outside the room. Okay, let's also actually just start using this specific thing. But before that, I just want to remind you guys start a even though it is a variable are the end of the day , it is just representing some sort off number on if you just have in sort of the a a normal constant, for example, or in this case, you are. And so I'm going Teoh going to be using the same rules. Ah, the same rules apply on you. Get the same answer out. Okay. Start our first house on. If you actually remember, we there the specific question in the previous lecture again we're going to do is lose again. So air is about one overdue again. One is in the numerator, so you have to court this inside off the route right next to the A. OK, so that is what you do on two isn't the denominator, so it comes outside of the route. OK, so it is actually quite easy now on to our second task. All you have to do is fill out of the box is okay now a recent 1/5. How are you actually going to be writing this again? One isn't a numerator. So what happens is that the new nature comes inside off the route on the denominator, which is five is just going to come outside of the route. Ok, ok. As you can see on the street, five comes outside the room R one comes inside the room. Okay, so it's actually quite a nice way to remember this. The answer just comes out to be a good effect through Aren't that impact is the answer. Okay, so good. There's move onto Artur. Task on this may seem a little difficult, but in fact it is really easy. All you have to do is find out of the boxes. One again is in the new manager. So you put that one inside of the room right next to the eight. Okay, you can falls over. Do you want to think about it? Okay, so we put the one inside of the route right next to the eight and 47 comes our side through . Okay, so that is, in fact, the answer now on to our throat as a reserve power 3/7. Now, before hard, we already were discussing ones in the numerator on it actually isn't a big deal. All you have to do is support three, which is, like any number, a number that you see in the new manager. Yes, Judge. What? You're just going to be putting dart inside of the room right next to the A. Okay, so you do that are the seven just comes outside of the route. OK, so this is actually quite easy. So this is a few, um, which is going to be, uh, like, the entire thing is being seventh router. Okay, so that is going to be our answer. That was all from my side. Thank you for watching on. I really, really hope you learn something. 26. Interesting Results From The Basic Indices Laws | Part 4: Hello hand. Welcome back. There's going to be the fourth part off. I was just trying to get some really interesting reserves using the three basic laws that we have already started. Okay, so the first thing that I want to be discussing this lecture is that let's say you've given some question as shown on the screen. So they let's say they say they are a rich the power you is just any number. Okay, So any number any variable orations are you, which is us against them? Some number is equal. Do at the same base a freshly the power we Okay, now, as you can see over here, the only thing that is different in this case are the powers. Okay, so you on, we are different, but they have the same bases. But in fact, what happens over here is that you can just equate the powers together. You can say that you is equal to week on what? Actually, just let's actually just make an example on Let's try to solve this specific example. So let's see your given the public question two years poverty and is equal to three. Race the race to the power of five X. In this case, all you have to do is equated the powers together 10 and five X Just sport, then instead of the u on d sort of it sort of reduced support. Five x. Okay, so I know you did That for 10 is equal to five X is what we're left with on all you have to do is solve for X. Okay, so you can actually do that. So tender Bible five God is able to do so accessible to do you found the value of duty off X. Okay. So in our second statement, we have, like, made a slight modification of head over there. We have the powers equal, but the bases are different. Okay, In this case, we have a reason for you equal to be some number from different number of different base racing power. Same power. You okay? So what happens in this case is that you could just say that the basis are in fact equal. Okay. And then you got a great not so let's actually go to a national example. Thursday have given the following question A squared is equal to 10 square all you have to do is say that a is equal to 10. Okay? And when you do that, like you can you just You just found out of the value of a Okay, So there's all from my side. Thank you. Watching on I really, really hope you learned something. 27. Surds | What are they?: Hello and welcome back. Today we're discussing serves because they actually quite come up quite a large and algebra . Okay, so there's actually go through the definition on where the definition says that any expression, not kind Britain and its exact form or quantity is, in fact or a certainty on some examples are by squared if you square of three and swear to five ants on Ah, the they're just wore examples right in front of you. And the word expression over here is quite important because these are not, in fact, some numbers. These are they are numbers, but in fact, they are being They have some operation being performed on them. OK, so it doesn't take the example of by, um, first of all. So the word of the the mathematical symbol are thing by can return in two ways. You can use the English actress B and I are the symbol, right? Which is right. Decides the guy. Okay, so these air do ways of writing by on if you actually put this inside the calculator, my cover say the the answer of pi is equal to 3.141592654 Martin Saad, This is not the answer. If I for 3.14113 point 1415926 by four I can not just say that this is equal to Pi because the calculator house just a normal amount of memory that can store. So this is a really good approximation, but this is not In fact, the exact quantity is nor the exact value of pie. Okay, so again they're taking the example of square root of do. The calculator comes out with the falling value 1.414 to 13562 But again, in this case as well, this is not going to be. The exact value is about this is, in fact, a really good approximation. Spirit of three gives similarly evolving answer. Okay, But, um, what do you actually mean by exact value than the fact is that if you port skirt of four, OK, it gives out an exact value off do. Okay, So what I can actually say is that squared before has the exact Well, you You do okay on that? Is there one of the reasons why I can't say that our sport before is assert its where the four count be Acer because it hasn't exactly OK, So we have the expressions were before on it has an exact value equal produce. So this is not going to be a certain. But if you have squared of seven, which is in fact, a certain it doesn't actually, um, the the of the quantity that the Taliban Iraq experts out is 2.645751311 But in fact, this is the only a good approximation. This is not the exact quantity, So there's going to be a certain Okay, so, um the so this is actually all there is to search. Thank you for watching on. I really, really hope you learned something. 28. Surd Problems | Solved!: Hello And welcome back today we're just going to be discussing problems involving Certs armed three only reason why I have the A and D written right besides the third is because capital has actually performed this task for you. But some teachers actually warned to give questions, so we have to sort of know how to solve these questions for now. So the possible question that you can get is like they might say, Like, try to simplify desert several by the falling serves squared. Afford to here, try to simplify that. Okay, so how are you going to be doing that? So let's actually go through the steps involved in trying to solve some questions similar to what you see on the screen. OK, so let's say you want to solve square to 40 or something. So the first step is do you have to recognize the square? So, um, what I'm actually saying is that two squared is equal before on three Squared is a good nine on so horse square to think the 16 all of these numbers 25 36 49 extra. You have to, like, sort of remember them so that when you see them, you can perform step do on them, which is due, uh, just to use a property to get rid of the squares. Okay, so let's actually let me demonstrate what I was actually saying. So this is the biggest question that way. Saw Square. Odo, 48 now simplified. Assert as the question. So what I, in fact do is I know that 40 year can Burton in due by, like, multiplying two numbers together 16 and three. So I do that. And then I remember that my guards 16 is actually just a square. So I can I can break these two down and say that squared of 16 is just impractical before and then say four times European Jessica 403. So this is involved. The simplest Doc Dysart can get on. We are going to say that these are, in fact, equal. Okay, if I don't score to 48 in terms of decimal numbers, that, in fact was would never give me a, um, proper exact quantity. But 403 is the exact quantity. Ah, like similar to what the answer would be if I wrote square root off 48 Okay, so this is what we're going to do. Now. Let's go through these steps step by step. So the first step is to recognize the square. So I have the most important squares for the specific task written right in front of you once. Where Do Square Three squared all the way up to nine square. Okay, so we'll have to go through them one by one. So one squared is just, in fact, equal. One two squared is equal to 43 squared is equal. Do nine. Okay, so four squared is equal. 16 5 squared is equal to 45 6 squared is equal. 36 7 squared is equal to 49 8 Squared is equal to 64. On our the end, we have nine squared, which is a cool to anyone. Okay, so these are in five the numbers. Now, if you see, uh, then you perform step two on the step to as, for example, the rule. Okay, so they're saying we have the following number 50 right in front of us on the steps. Involvements in step two are trying to think of two numbers are First of all, this is just try to think of two numbers I thought you can use to break down 50 that when you multiply those two numbers, you get 50 on the first thing that you might think of his stand and fight. Right? So five times standards. Even if 50 aren't, you could write that down part over. As you can see, 10 and five are two numbers that are not squares again. So what do you do it? Simplify this thing even further? So let's break down 10 and you can actually do that on breaking that down. Gives us a forming things or two times five times five against in the 50 I can actually see the square right in front of me five times five. That is, in fact, equal 25 25 is in fact, a square. So what I can actually do is if they give me a question saying that, what is the simplify the search square to 50. So what I can do is I I can say that. Okay, so 1500 in the following way to times 20 life on that I can break those two things down and say that 20 sweater, 45 was just people to five on. Then I can write the final answer down five times under two on I can be done with the question, OK, so that it either doesn't like these simple steps more and right. Just all the questions. Um, practice him early on. You can, in fact, just keep on doing the questions. Okay, So thank you were watching on I really, really hope you don't something. 29. Exponential Functions | What Are They?: Hello and welcome back Today we're just going to be discussing exponential functions what they are and work. They're not and is going to be a really brief introduction really about it. So on the screen, I have for examples. So the 1st 1 is do racial about ex. The 2nd 1 is fibrous to power two x. The 3rd 1 is E Richard Power 0.7 x before one is 0.5 regional power negative X on in all of these four cases, the thing that make up on exponential function is first of all, Carl as the base now, which is due in the first example. Okay, in the independent variable, which is negative X in the fort example on similarly X is going to be the independent variable in the first example. And the important thing is that the variable portion overhand this cannot be a constant number. Okay, the e that you see on it on the screen when the third example is not a variable, it is just a constant number, but it is so long that you don't actually write it out. You just denoting their dinner. The letter e for that Okay, so if you write it out in mathematical form, this is what you get. Now, the first portion which is the left, are inside. I don't have to. Actually, the national the exponential function part does. That is just denoting that this is a function. Okay, that would have you write it from on on the right inside. That is how you write out an exponential function. A race to the power X on eight over is just going to be any normal number. Okay, Any normal number. While X is the actual important part that is going to be a variable. Always. Okay, so again, a escort as the base on this X is going to be caught as the independent variable. Ok, now let's look at where the values thes both things can take. Now, that's like a look at the base. First full. Now, a needs to be greater than zero, which is the base. Okay, Now, let's actually do a number line out of a window, it over it on on the left hand side, we have the negative numbers in the middle. We have zero. And on the right hand side are all the positive numbers on a can take on any positive value except for one number, which is one again. So except for this specific value, they can take on any value. Okay, Now that means that they can take all the value of 10 2030. 44,000. 5000, 10,000 Any number except for one on any segregated zeroes over. Can I also take on the value off 0.10 point two or 13 etcetera. Ok, now, what about the independent variable which is X in this case, X can actually take on any value as long as it is on the real number line. As you can see on the screen, all the sherry portion it can take on. So negative 5000, 10,000 Any really large negative number or any large positive number. Okay, so that I can actually you extent take on that value. But the only thing that you have look out for again is that the specific thing adjusting on the screen overhead there is no next mental function that is, or as a constant. Okay, do you receive over to We're just going to be called as a constant on. The reason for that is the do is over too. Is actually, just means are two times two is a sequel before and again, the X in this case is equal to do. But then again, I told you that the, uh, the X is going to be an a variable. Okay, now, But with a ridge is going to make a small change to make it into an exponential function. Okay, when we get that now, you can call this an exponential function. Okay? The reason for that is this is to raise the power to X. You have ax over here, which is again a variable. Okay, so there is a whole for my side. Thank you were watching, and I really, really hope you learned something. 30. Graphing All The Exponential Functions | What do they look like?: Hello and welcome back Today we're just gonna be graphing. Our exponential functions, which we have previously discussed and he was lecturer on, is going to be a religious, like, normal general overview about what expensive functions look like when you try to modify the , um, like the like. The base are the of independent, independent variable. I'm just offered. That we have used right now is called That's most. You should really check them. I would have always used the upper version. Ah, we have in the mobile APP version are they have been really good part is, like the first time the pictures that have used in this specific lecture. Um, that was me using the desktop version using a browser. Our this was really amazing to you. Should really check them out. Doesn't really have foreign trying to understand graphs. Um, when you're trying to understand graphs of any kind Okay, let's just actually begin the grafting process. And first of all, there's going to be a general normal exponential function tourist about X started, we have, and as you can see as you move from the left arm site all the way to the right hand side. By the way, the red line is actually the craft. The actions overhead we have the wax. Is we just a vertical one on? We have the horizontal X axis in this case. Okay, Okay. So as I was saying, uh, as you move from the left hand side all the way to the right hand side, it just seems like you're trying to climb up a hill or a mom. So we're just going to be using this metaphor and trying to understand how these graphs are behaving, how they're actually changing on. We're just going to be first of all, increasing the base. We're just doing this case, OK, we're just going to be increasing that on. Let's actually just see what happens, OK? So as you just increase as i I as I just increased the base from 2 to 4, as you can see, what happened was that we are against, like, nothing significantly different happening instead, like only the only thing that happened was that the slope is now actually quite air steeper . Right? Okay. As you can see, it was like slightly less d are now is a lot more steep. Okay, but again. If you actually look at it, we are. Feet are going to be passing through the 0.0 number one, which is a while, which is the y intercept, which has a silver door right in front of it. Our fear it is actually going to be passing through that regardless of we have to writable Rex or Forest Pyrex. Okay, Presidential, actually, let's just proceed with increasing the base. And as you can see, the only thing are changing as the slope in this case, and this is getting really, really hard for us to climb up the hill. OK, Aren't this is like a really big number raised by Rex on as you can see. Ah, the only thing that is happening is just like reason days on the paragraph is starting to catch. The waxes aren't also the X axis. First of all, the x axis and then the waxes. And this is actually just happening. So what we just covered right now we have the number line Brighton Part of us is all the numbers from greater than one all the way up repulsive infinity. This is like the general trend are the function are going to be covering are so let's just actually cover this visited portion out and then we're going to be done with the bases. Okay, So again, job on fiber is going to be starting from zero point flying Power X is going to be the normal graph on then. First of all, we're going to be increasing the base from 0.5 up to 0.99999 You don't actually trust one musical rex on. Then we're going to be again, starting from driven five, all going all the way down to 0.0. That is there. Is there something a lot off? There's after the hard one again, We can't touch the civil rights. So first of all, they just go up. And, as you can see as we go up the specific numbers from the port 50 we have your process. Right now, all that is happening is first of all, it looks like we're trying to climb down the mountain again when we a mountain or hill when we move from the left hand side all the way into right outside. Okay, Bar. The thing is that it is actually getting quite easier for us to climb down because the Slovis actually decreasing on. How do I know others to get a smoke is decreasing darks Because it is becoming easier for me to climb down or up a specific hill if I'm trying to move from the left hand side all the way to the right hand side. Okay, so that is how I know now the slope, It's increasing or decreasing on, as you can see, um, this is actually just getting really This is running like dissolves. It looks like a normal straight line right now. Is there a 0.999 x? This is actually doesn't look like a hill. This looks like you have You have passed a hill for, like, a kilometer or something. Really long distance. And so now, just actually go now and from their own five. Let's just go down. As you can see, this looks like we are and a lot of trouble if we wanted to climb down The specific man was this location. Career is the slope is really increasing quite a lot. As we move down, what happens again? I could happen previously was the number. So sorry. The graph actually just starts to hug the axes. Okay. As you can see, this is really like, First of all, I just hugs the y axis, and then it just hugs the X axes right to I mean, it is just a tosh, and there's gonna be really hard for you climb down the mountain going from the left hand side. But I turned Sorry. Okay, so there's no actually increases. But again, in all of these cases, the specific 0.0 comma one were always our feet are always going to passing through the are specific point, which is something that all of them happen. Comments. So that just actually go through the independent variable, which were again the powers are Let's just try to modify the values and see or get. And again, if you can remember, we can have any value, uh, with regards to, like in the independent variable. So they just have to start with The negative ones were so far purchaser again going to be using this report. Fighters of our X, our baseline. Sorry, Arby's exponential function iron. So let's just actually make something out of it. So there's are negative in front of it. And as you can see, he's number five again basis saying the like. The power is different right now. So as we now, as we ordered the negative sign do the power which was open fires direction now it was the fourth I raced our negative X. What happened was that if you put a mirror on the Y axes, um, this is what you're going to get. There's almost think this is actually called as the reflection along the Y axis. Okay, I'm gonna That is exactly what happened. I'm something interesting just for, like, general knowledge you re support X has the exact same graph on Let's actually see why that is in a short time. Um, OK, so do it about negative X Again, we have tourist of our X. This is like the graph of tourists forex. And as you can see, if you reflect on the wax is you're going to get two hours of our negative X on again. General, all of Europe on fibers to Power X has the same craft. Okay, so, like small stuff that I guess helps out any every now and then, so I just actually increased in different variable right now. We have Rupert, if I raise about one X okay. Nurses increased our when we increased from one x 2 10 X. As you can see, what happened was that the slope increased quite a large. But again, we are still passing through the point joke on my one. Okay, as English. Further, this is like almost this is like catching the actions even more than we like previously were able to make the number touch, make the ground touch. Okay, so there's actually do the officer thing right now. Let's just decrease the intern thing, and this is most likely going to be causing the okay. Exactly that happened. Uh, this soap is actually decreasing on Is getting really, really easy for us to, uh, actually dry it out and again. Driven one. This was your or one X are not one of your fibers. About one X. That's not it. If you're born five rich, the powers Europe on one X in this case. Okay, So, house agency, we are getting, um it says it is just getting easier for us to climb down the specific mountain. All that had on that's to, actually. Okay, well, let's start about it. Who was one? X and this is decreased Is right now aren't as you can see again. All that's happening is are just getting easier for us to climb the mountain over there. Okay, So one final thing wonders about her ex. Isn't art an exponential function? It's actually just a normal straight light. And this is what I got when I, um, actually put this and that's most okay, so that is the reason why we don't actually called this an extension function you're watching hand. I really, really hope you learn something. 31. Properties Of Exponential Functions | What Are They?: Hello, and welcome back today we're just discussing some properties that are expensive functions exhibit? Aren't letters actually go through? The 1st 1 right now on that is that the graphs are always doughty. Passing through one single point, which is your comma. One on what we actually mean by that joke over one is, um, us trying to say that the point is on the x axis, not at zero on on the y axis. That point is one. Okay, so zero comma one means this specific point. OK, but it's going to be moving to that point right now. So this is a graph of two words about actually going pretty familiar with that. Would this arm the other graphs? And be sure because this was what we discussed in the previous video. If you haven't war started, go and wash that out. Okay, So this is the This is the function, just the expression of luxurious. But Rex is the graph off towards more wrecks. And as you can see, this is the point that I was talking about. So zero comma one on. Just like another graph that we also discussed in the previous lecture. 016 Racing ball, Rex. And as you can see, we have the point there again. Zero comma one. And as you. And remember, I was always talking about this visit important. All of the official functions are going to be passing through this one point because I've actually heard in their down. If you can see a disempower zero is always going to be giving us the answer one regardless off what is as long as it is inside a you know, inside the expression functions boundaries. Okay, so what is the Oh, that is all for the first property. Now we're going to move into the second property. So where does the second property actually state? So the second property, Cesar de function Africa exist means function effort of the function. A race to the Power X. Okay, The expense of functions, if a is greater than one was the bays F is going to be called us at increasing function. Okay, if a is between is between the values zero and one, you are going to be calling this as a decreasing function. Okay, So what do I mean about our 16 rest of our X starts? the graph that you see on the screen right now on this is going to be called us an increasing function. Because why 16 is greater than one? That is the reason why on if we see the following graft after you see on the screen zero Pawn six raced a power axis of the graph. This is going to be called as a decreasing function again. The reason being because this as between zero on one. Okay, so that is all from my side. Thank you were watching and I really, really hope you learned something. 32. Absolute Value | What Is?: Hello. And welcome back today, we're just going to discuss saying absolute values on the thing that you see on the screen . The X are with the Tuareg alliance. That is how you say the absolute value off X. Okay. Doesn't actually go through definition. First of all, So the definition, actually just Cesar the absolute value of a where is going to be any normal, real number, like on the number line. Okay. Not anything. Fancy, normal stuff. Eyes going to be a for when the value of Adrian zero. I was going to be negative A or on the value of 1000 year. And probably because because, yeah, I shouldn't understood. None of that is actually go through the normal human language stuff that I personally love because, like like this is Waters should be like a simple terms. Just explain what he just said. What I said in simple terms right now, so that today we have the value 45 we have the number 45. I'm going to find out of the absolute value of that. So that is going to be equal to 45 because 45 No, don't say the value is number is negative. 45. Now you want to find out. The absolute value of that I'm not is going to be equal to negative. Maybe 2 45 You know why? Because nearly 45 lessons, right? So what actually happens is that you get 45 out there. So in normal, simple human terms, this means that you just take any number that you see on Just make that into a positive number. So let's say you have the value. We have number negative nine in front of you. What is the absolute value off negative? Nine night. Where is the absolute value off? 9999 Not is just equal with 9000 line under 99 What about negative? 99.99 And again, they are just going to be able to 99 or 99 for about 99 for nine hours. Equal 99 or 999 by five Rz will do 95. What about negatively Drive a fine Cars just go to be able to line my fight when you're 495 negative job or nine flying Where the after Williams Art 0.95 And that is literally how you do all the after party numbers. Really easy are not, is basically all there is to have some values off any number anymore to see, just convert that into a positive number regardless of where do you see positive negative spin were down into because of number. Okay, so take your washing and I really, really hope you learned something. 33. Absolute Value Properties | Part 1: Hello and welcome back. We're just going to be discussing some properties with regards to, like, absolute value. There's going to be the first part. Watch out for the second part as well. So, first of all, the first property that we are going to be discussing the negative aren't the positive off a specific value when we're trying to find out the after value of both of them are going to have the same answer. So where do I actually mean by that? If let's say we have the following number negative five on we have the like is in this case is going to be fine. So what? I'd say we have negative fight and five, the absolute value off Both of them are going going to be equal to five. Okay, let's say we have the following numbers. Negative 5.5 and 5.5. Again. The answer. The answer off Both of them is going to be equal to 5.5 again. We have negative 99 by 23 on 99. Viber 23. The answer to go to them is going to be positive 99 by 23. So this is like the first property in this case is going to be equal. Positive they are. That is all there is to the first property. Okay, negative. Aren't the number the number honest negative are going to have the same value in this case again. Just a quick reminder. There's going to be equal to positive A Okay, now the second property. The second property access here is that if we are, we have an absolute valley, which is a product off to individual numbers. Well, the answer can actually you're gonna get the same answer if you like, have the numbers, you take the absolute value of them individually, and then you multiply them. Let's look at an example. Let's say you have your given the following example. We have negative five times stand inside of the absolute value. And then we have negative five individually being like having the, um we were taking the absolute value of negative five, and we also are taking in the absolute value off. Then individually. So what do we actually get? Negative five grams stent. We're going to be solving the left hand side. First ball, negative. Five times stand. We get the answer. Okay. We're actually just moving a little faster than I wandered. So negative five times stand. We get negative. 50. Okay. On the absolute value off negative 50 is equal to 50. Okay, on the right hand side, we have negative five. And the absolute value of negative five is equal. Five okay, on we have also we also have 10 on the after value of 10 is going to be equal. Do then. Okay, so we get five. I understand if any of this seems a little bit confusing, you have the wars previous radio, which is in regards to after value and how? Well, first of all, what it actually means on then how do you have to find it out? So this is this is actually important. If you don't know that uses one stock video. So five times 10 that's just going to be equal to 50. So we have 50 on the left, our side, and we have 50 on the right hand side again. Same answer. Different way off. Doing this. Okay. Stars all days There is from my side. Thank you Were watching. And really, really hope you're on something. 34. Absolute Value Properties | Part 2: Hello and welcome back. This is going to be us discussing the properties again off absolute values. There's gonna be second part. So starting with the third property, um, which actually stages are if you have two numbers which are being divided together inside and after value, we're going to get the same answer if you have them being individually. First of all, ah, have their observations taken out and then divided together. So I was actually just moved through a tangible example. First of all, so let's say you're given the following things negative floor and do on on the left are inside the answer for small. It is moved to the left hand side. So the answer is going to get is what we call the negative to on the absolute value off Negative two is to there. Now, let's actually go through the right hand side now. So the officer value off negative, for we have previously discussed this. If you don't actually understand some of the style for you off, he wants the previous videos. Okay, so the after value off negative for that is equal to four on the absolute value off to positive two is going to be again equal to do so. Four divided by do their your answer that you're going to get is equal to do so over here, Like we have proved that their property do is equal to 2/3 Roberti prove OK, so that is all there is to the third property moving on to property number four on the four property states that if you have an absolute value, which is a combination off two numbers being out together, the answer that you're going to get if you individually have the absolutely taken out and then do the addition Well, the right hand side is going to be is going to be greater than the left hand side. We're going to be moving greater than or equal to. We're going to be moving through these unusual things step by step. We're going to be actually washing the all the Devo cases. Okay, Okay. So, virtual there's move through the equal one case. Okay, so let's say we have the value off a equals three and the value of the equal to two so triplets do not is equal to five were actually solving the left hand side first of all, So the after value of five is going to be equal to five again. On the right hand side, we have after value three on the absolute value of two. Again, the answer off over here is going to be equal to three and two on money are three plus do. The answer is five. And this this was this was the case in which we get the equal out, sir. Now we're going to be moving to the example when we get when we were in the right hand side is actually greater than the left hand side. Okay, So negative to me is the value of a and the value of these 1/4 to positive, too. Now that our them together for 12 left outside negative three plus two, you get the answer. Negative one on the after value off. Negative one is going to be equal to positive one. On the right hand side, we have the absolute value off negative three on two. So the after value off negatively that is just equal to Paul's victory on the after party off positive two is just going to be equal to positive too. so three out of two, you get five. So one is less. Invite on data is exactly the case. So that is all for the fourth property on you watching. And I really, really hope you learned something.