 Factoring, factoring, factoring. Now, I mentioned in the previous video that there is six types of factoring that we're going to talk about, right, two of which we've already talked about. One of them is the, the first one was the GCF and the second was the simple trinomial factor, right. Now, we have four more factoring techniques still to go. The one we're going to talk about right now is the difference of squares. Now, if you haven't, if you don't know how to do the first two types of factoring, which is the GCF and simple trinomial factoring, for sure take a look at series 3A because all I'm going to do right now is just build up from that. There's going to be a little bit of repetition, a little bit of just a reminder of what sort of things are, but it's mainly going to be basically building from what we had before. The difference of squares is the simplest type of factoring there is, but it's, there's a lot of misconception with it, okay. For me it was anyway when I first learned it. Most, the most common, common way that I've seen it presented is a squared minus b squared, right. So you go, it's a squared minus b squared. It's, it's basically the difference of squares. What it means is if two things are subtracted from each other, you can factor them out in the following form. It comes out as, if you have anything, a squared minus b squared. We'll talk about this a little bit further, but it's mainly presented this way. If you have a squared minus b squared, if you want to factor this out, basically meaning you want to break this up into things multiplied together. That's what factoring means. You're going to try to break something up that's got additional subtraction to it, and you're going to have terms multiplying each other to give you the same thing, right. So if you want to break this thing into things multiplied together, what it turns out is, is a minus b brackets times a plus b. Now it doesn't, now it doesn't make a difference if you write down a plus b times a minus b, as long as you're switching between the plus and negative, okay. Now if you want to work this out to make sure that you end up getting this, when you foil this out, what it means is you just go this times this, this times this, this times this, this times this, right. So you foil it out, you multiply the thing through. So if you foil this out, a times a is a squared, so you're going to go a times b is a times a, a times b, so you got plus a b. Negative b times a is going to be negative a b, and negative b times positive b is going to be negative b squared, right. And what happens, what you have here now is a squared plus a b minus a b minus b squared. Well a b minus a b is just going to be killing each other off. So in the end you have a squared minus b squared, and this gives you that back again. Now this is just for the check, okay. If you're factoring this guy, I've seen some people do this, when you know you give them a question say factors something like this, they end up factoring it and then foil it back out again and end up here and they leave this as a final answer. That's not the final answer. If they say factor it, this is the final answer. For the longest time when I first learned about this method, I thought it only worked for things that were perfect squares, okay. That's not the case. This method works for any two things subtracted from each other. So if you have something minus something else, okay, to factor that all you do you say the square root of the first thing minus the square root of the second thing all of it times the square root of the first thing plus the square root of the second thing. So the way you can think about it is a squared minus b squared is the square root of a squared minus the square root of b squared times the square root of a squared plus the square root of b squared. And the square root of a squared is just a, the square root of b squared is just b. The same thing over here, right. So that's why it equals. That's why it equals the square root of a squared minus the square root of b squared. That's why it equals a minus b times 8 plus okay now to make this clear let's go do it with symbols basically squares we said that it's a squared minus b squared and that is again for me was a misconception the best way that I've learned to think about this to remind myself that any two things subtracted from each other you can factor them out into the square of the first thing minus the square of the second thing times the square of the first thing plus the square of the second thing okay and the best way you can do it is just visually think of a square that's what the difference of square means there are two different types of squares okay and squares in mathematics we symbolize it as right if you have one square and square in math a lot of books I've seen the way what they do is square represents you being able to put anything you want in there so you can put anything in here minus another thing two boxes subtracted from each other the difference of squares right two things like that if you get anything and it could be a gigantic term here it could be a gigantic function right you can still factor so you can take two sections of anything and factor I think I want ballistic good colors here it looks a little confusing but anyway if you have two squares there are different squares different things in here in here than it is in here because if they were exactly the same thing that thing which is equal zero right if you simplify them which is equal zero so if you have two different things subtracted from each other it's the square of the first thing minus the square of the second thing times the square of the first thing plus the square of the second thing and that's for anything and there's a lot of questions I've seen for difference of squares where they're really gigantic confusing equations or confusion confusing expressions that they want factor and a lot of people get stuck with them because they they have a hard time grouping things together okay and we'll do a few examples where we're grouping different things together okay so let's just start off with some simple simple examples and continue from there and this method two things subtracted from each other like this two things added together you cannot factor them okay so if you have a box plus a box so if you have two boxes added together if you have two boxes added together you cannot factor this okay and we'll talk about why this is when we start going into the equals sign when we got an equation where this side says equals zero which is what we're really going towards right factoring it's just a tool that we have to be able to solve equations because equations where we want to be those are our models of something or that's our way of calculating whatever it is that we want to calculate right so factoring when it comes up to straight factoring it's just one step a for one step for us to be able to solve equations and to get answers and solving equations means finding our eccentric sense right as we talked about before multiple times right and all of that stuff we talked about in series 3a right so right now let's just go do a few examples of this just just to show how easy it is and it is this this for sure as far as I'm concerned the easiest factoring technique there is and for some reason a lot of people get it wrong because I guess it's it's an assumption for me was an assumption that when they said a squared minus b squared they meant every anything has to be a perfect square not true any two things subtracted from each other even factor thus okay