Polynomials review:

Multiplying binomials using algebra tiles:

We have 1 tiles, x tiles and x^2 tiles, the negative tiles are in red, and the positive tiles are in wither green, blue or yellow.

For example (x+2)(x-2)

We multiply the x (the green long tile) and get x^2 , and we multiply the +1 (yellow tile) by the x tile and get x, and on. It goes as the same for the -1 multiplying by x, except we get red x tiles, because it becomes -x.  So then we get x^2 -2x+2x-4. The 2x cancels out the -2x, so we get x^2 -4. we can check using FOIL.

 

Factoring trinomials:

Here, we have trinomial x^2 +4x+4. We use the multiplying rules, and we can factory x^2 into two x tiles, and we can factor x into 1 tile and x tile, we factory 1 tiles into 1 tiles. So then we get (x+2)(x+2). We can also check using FOIL.   Nothing cancels out because they are all positives.