Question

How do you factor `200x^2 + 800x +800`?

Answer 1

`200x^2+800x+800 = 200(x+2)^2`

Explanation:

All of the terms are divisible by `200`, so separate that out first:

`200x^2+800x+800 = 200(x^2+4x+4)`

The remaining quadratic factor is a perfect square trinomial:

`x^2+4x+4 = (x+2)^2`

Look at the pattern of the coefficients. It might remind you of this:

`144 = 12^2`

This is no coincidence. The coefficients are all small enough that no digits are carried during the multiplication of `12xx12`, so the digits `1,4,4` of `144` are the coefficients you get when you square `(x+2)`.

Putting it all together:

`200x^2+800x+800 = 200(x+2)^2`