# How do you factor 9x^2y^2-z^2 ?

Jul 6, 2015

This is a difference of squares:

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

#### Explanation:

The difference of squares identity is:

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

In our example, let $a = 3 x y$ and $b = z$...

$9 {x}^{2} {y}^{2} - {z}^{2}$

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

$= {a}^{2} - {b}^{2}$

$= \left(a - b\right) \left(a + b\right)$

$= \left(3 x y - z\right) \left(3 x y + z\right)$