# How do you factor x^2-81?

May 18, 2016

${x}^{2} - 81 = \textcolor{g r e e n}{\left(x - 9\right) \left(x + 9\right)}$

#### Explanation:

For the general case:
$\textcolor{w h i t e}{\text{XXX}} \left({x}^{2} - {a}^{2}\right) = \left(x - a\right) \left(x + a\right)$

$\left({x}^{2} - 81\right) = \left({x}^{2} - {9}^{2}\right)$

substituting $9$ for $a$ in the general case gives:
$\textcolor{w h i t e}{\text{XXX}} \left(x - 9\right) \left(x + 9\right)$