# How do you factor 169a^2b^2-16c^ 4?

Jun 12, 2016

$\left(13 a b + 4 {c}^{2}\right) \left(13 a b - 4 {c}^{2}\right)$

#### Explanation:

To factor $169 {a}^{2} {b}^{2} - 16 {c}^{4}$ we must first recognize that this is the difference (subtraction) of two perfect squares.

$169 {a}^{2} {b}^{2} = \left(13 a b\right) \left(13 a b\right)$
$16 {c}^{4} = \left(4 {c}^{2}\right) \left(4 {c}^{2}\right)$

When we factors the difference of two squares the binomials always have one $+$ and one $-$.

$\left(13 a b + 4 {c}^{2}\right) \left(13 a b - 4 {c}^{2}\right)$