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

May 12, 2016

$200 {x}^{2} + 800 x + 800 = 200 {\left(x + 2\right)}^{2}$

#### Explanation:

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

$200 {x}^{2} + 800 x + 800 = 200 \left({x}^{2} + 4 x + 4\right)$

The remaining quadratic factor is a perfect square trinomial:

${x}^{2} + 4 x + 4 = {\left(x + 2\right)}^{2}$

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 $12 \times 12$, so the digits $1 , 4 , 4$ of $144$ are the coefficients you get when you square $\left(x + 2\right)$.

Putting it all together:

$200 {x}^{2} + 800 x + 800 = 200 {\left(x + 2\right)}^{2}$