Factoring two Binomials

When expanding two binomials, you create a chart so that the binomials are on the outside, and you multiply them inwards to get your answer on the inside. In this model, it shows:

(x+2)(x-2)= x²-4

As the red sides are negative and the positive sides are green, blue and yellow. You can see that there are an equal amount of positive and negative x’s in the result. Because of that, the x’s cancel each other out because your adding 2x, then subtracting 2x, which leaves you with 0.

Simplifying a Trinomial

 In this trinomial, x²-x²+3x-3x (or 0), it can be simplified back into the binomial/trinomial it originated from. When you start, I find it easier to try to figure out one side first. If we start with the left side, you can tell that it has to be 2x because you need and x to get a x². To coninue we can assume that the left side is (x-x). On the top side we can use the x²s to figure out the first x. We can guess that it’s -x because a double negative is a positive and a positive and a negative is a negative.

We can then look and see that since on the far right side, they are all single x’s. With that we know that they are 1’s/ Since our first x is positive, we can see that it’s 2-1. So in the end, we simplified it to (x-x)(-x+2-1).