# How do you factor x^2 + 6xy + 9y^2?

May 20, 2015

You can factor this by grouping.

The coefficients of ${x}^{2}$ and ${y}^{2}$ are, respectively, $1$ and $9$, the product of which is $9$, which, in turn, can be factored in $\left(3\right) \left(3\right)$.

So, we can rewrite our function as

${x}^{2} + 3 x y + 9 {y}^{2} + 3 x y$

and factor it by two groups of two terms each:

$\textcolor{g r e e n}{x} \left(\textcolor{b l u e}{x + 3 y}\right) + \textcolor{g r e e n}{3 y} \left(\textcolor{b l u e}{3 y + x}\right)$

We can see that the parenthesis of each term are exactly the same, so we can use them as the common multiple of the whole equation that are multipling the rest:

$\left(\textcolor{b l u e}{x + 3 y}\right) \left(\textcolor{g r e e n}{x + 3 y}\right)$

Done!