# How do you factor 81x^2 - 36y^2?

Jun 21, 2015

The answer is $9 \left(3 x + 2 y\right) \left(3 x - 2 y\right)$.

#### Explanation:

Factor $81 {x}^{2} - 36 {y}^{2}$.

Factor out $9$.

$9 \left(9 {x}^{2} - 4 {y}^{2}\right)$

$\left(9 {x}^{2} - 4 {y}^{2}\right)$ is in the form the difference of squares:

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

a=3x;#$b = 2 y$

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

$9 \left(3 x + 2 y\right) \left(3 x - 2 y\right)$