# How do you factor completely 9x^2 - 25y^2?

Nov 13, 2015

$\left(3 x - 5 y\right) \left(3 x + 5 y\right)$

#### Explanation:

Given: $9 {x}^{2} - 25 {y}^{2}$

The temptation is to do the following:
$9 \to {3}^{2}$
$25 \to {5}^{2}$

Using this we have:

$\left({\left(3 x\right)}^{2} - {\left(5 y\right)}^{2}\right)$

$\implies \left(3 x - 5 y\right) \left(3 x + 5 y\right)$

Does this work?

Check:

$9 {x}^{2} - 15 x y + 15 x y - 25 {y}^{2}$

Yep! This has to be the answer!!!