# How do you factor x^2+6xy+9y^2-25?

Mar 28, 2018

${x}^{2} + 6 x y + 9 {y}^{2} - 25 = \left(x + 3 y - 5\right) \left(x + 3 y + 5\right)$

#### Explanation:

Given:

${x}^{2} + 6 x y + 9 {y}^{2} - 25$

Note that both ${x}^{2} + 6 x y + 9 {y}^{2} = {\left(x + 3 y\right)}^{2}$ and $25 = {5}^{2}$ are perfect squares.

So the given polynomial will factor as a difference of squares:

${A}^{2} - {B}^{2} = \left(A - B\right) \left(A + B\right)$

with $A = x + 3 y$ and $B = 5$ ...

${x}^{2} + 6 x y + 9 {y}^{2} - 25 = {\left(x + 3 y\right)}^{2} - {5}^{2}$

$\textcolor{w h i t e}{{x}^{2} + 6 x y + 9 {y}^{2} - 25} = \left(\left(x + 3 y\right) - 5\right) \left(\left(x + 3 y\right) + 5\right)$

$\textcolor{w h i t e}{{x}^{2} + 6 x y + 9 {y}^{2} - 25} = \left(x + 3 y - 5\right) \left(x + 3 y + 5\right)$