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

Oct 7, 2016

${x}^{2} + 6 x y + 9 {y}^{2} = {\left(x + 3 y\right)}^{2}$

#### Explanation:

Notice that both ${x}^{2}$ and $9 {y}^{2} = {\left(3 y\right)}^{2}$ are perfect squares.

So we can try squaring $\left(x + 3 y\right)$ and see if the middle term works out as $6 x y$...

${\left(x + 3 y\right)}^{2} = \left(x + 3 y\right) \left(x + 3 y\right) = {x}^{2} + 6 x y + 9 {y}^{2}$

So ${x}^{2} + 6 x y + 9 {x}^{2}$ is a perfect square trinomial.

In general we have:

${\left(a + b\right)}^{2} = {a}^{2} + 2 a b + {b}^{2}$

So we can recognise perfect square trinomials by whether the middle term is twice the product of the square roots of the first and last terms.