ʕ•ᴥ•ʔ Solve Equations with Algebra Tiles: Easily Factor Polynomials

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Algebra tiles can be used to represent polynomials. We can also use those tiles to solve polynomials. In this lesson, we will try to solve some polynomials using algebra tiles.

Hi, welcome to this algebra question here. So once in awhile we might have to draw these little things to represent how the factors actually work. So, we have 2x right here times x minus 2. So, what you need to know is that this is actually one bracket by itself for the first one, right? So, x is the one that has the kind of longer shape but it's a little thinner. So, we're gonna do one over here and another one over here. Okay? Now if you remember, if it's positive, we shade it in, if it's negative then we can actually leave it empty. And sometimes vice versa, so it really depends on your text book and what your teacher says. So, in my case, let's just pretend that if you shade it in, it's positive. So I'm gonna go ahead and shade in my positive x right here and the positive x right here. So, by looking at this, from this point of view, that's x and that's x and you're adding them, so together it's called 2x and for the first one. Okay? And over here on this side I'm gonna draw a line over here and draw little line over here so that there's x minus 2 on the top. So it should be like x minus 2. But once again, the x is represented by the long rectangular shape right here so I got another long rectangular shape just like that. And again, it's positive so you just shade it in. The negative 2 at the very end is a constant number, so it's represented by little squares, so that little square right here is just going to be empty boxes. Okay? So once you're done with that, you're just gonna go ahead and actually figure out what's going to be inside. Okay? So, we got a bigger bracket right here and that represents the x squared and it's the shaded one. Okay? And we got another bigger bracket, I'm mean not bracket, sorry, that's probably called a square, right? And another x squared right here and we're going to shade it in and pretend it's positive. And over here we got long stripes right here and long stripe because they have to form the perfect rectangles. Okay? And, in that case, they're both negative, negatives, okay? So, in order to see that they're negative, negative, we need to make sure they're both empty, empty. That means, the final answer, if you actually go ahead and multiply these two guys right here, this is the answer, okay? So we're going to do the top part first and figure the bottom part right here. So, what's 2x times x? Two x times x is going to give you the 2x squared. So, we got 2x squared. Aha! We got two of them right there, see that? And, we also have the 2x minus 2, so it will be a negative 4x and that's why we got four long stripes of empty rectangles. So, I don't know if you still want me to show this to you, but let's go ahead and do the bigger square right there. We got one piece and another piece right here so that represents the 2x squared and we also have 4 more long rectangles that are not shaded in. That tells you the final answer you have is 2x squared minus the 4x. And this is just using the algebra tiles to represent the final answer. Okay? Pretty fun. You can try it on your own, okay? Thanks for watching.

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