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When expanding two binomials using algebra tiles, arrange your binomials so that one is up horizontal, and the other is done vertically. For example, when doing the equation (x+1)(2x-3), you will arrange the binomials like this. For all tiles, the red side is negative and any other colour is positive. First, multiply the x tiles. You have x(2x) which makes $2x^2$, so you use 2 positive $x^2$ tiles. Then you look at x and -3. When you multiply these two, you get 3x. So now you know that the final answer will be $2x^2-3x$ and something. Then, look at 2x(1). By multiplying, we know this is 2x. If we add 2x and -3x together, we can find that the x value will be -1x. Finally, we look at the two constants, 1 and -3. When multiplying, we get -3. So our final answer will be $2x^2-x-3$, much like this. When factoring a trinomial, you simply do the opposite of the steps you took when expanding two binomials. For example, when we have the trinomial $-2x^2+5x-2$, we lay the tiles out, the $x^2$ to the top left, and arranging the rest of the tiles to make a perfect(ish) rectangular form like this. Firstly, you must realize the $-2x^2$ is negative, therefore one of the x must be positive, whereas the other one is negative. However, we can also see that -2 on the bottom right corner is negative too. Now we must look at the 5x. 4x is stacked together on the bottom left side, and there is an x in the top right corner. Because of this, we can use common sense to realize that the 2x on the top will be negative. Using this information, we can find the x on the side will be positive. Furthermore, because the lone x on the right side is positive, but we know the x on the left binomial will also be positive, we know the constant on the top binomial will be +1. Now we have one binomial -2x+1, and we know the x on the left binomial is positive. Finally, using the process of elimination, we can find the constant on the left binomial will be negative with a -2.

So, we can find the two binomials will be (-2x+1) and (x-2), much like this. 