Polynomials review:
Multiplying binomials using algebra tiles:
We have 1 tiles, x tiles and 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 , 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 -2x+2x-4. The 2x cancels out the -2x, so we get -4. we can check using FOIL.
Factoring trinomials:
Here, we have trinomial +4x+4. We use the multiplying rules, and we can factory 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.