# How do you factor the expression a^4 - 81?

Dec 9, 2015

${a}^{4} - 81 = \left({a}^{2} + 9\right) \left(a + 3\right) \left(a - 3\right)$

#### Explanation:

$\left({a}^{4} - 81\right) = \left({\left({a}^{2}\right)}^{2} - {9}^{2}\right)$
and is therefore the difference of squares with factors
$\textcolor{w h i t e}{\text{XXX}} \left({a}^{2} + 9\right) \left({a}^{2} - 9\right)$

but $\left({a}^{2} - 9\right) = \left({a}^{2} - {3}^{2}\right)$
is also the difference of squares with factors
$\textcolor{w h i t e}{\text{XXX}} \left(a + 3\right) \left(a - 3\right)$

$\text{---------------------------------------------------------------------}$

Remember: Factoring the Difference of Squares
$\textcolor{w h i t e}{\text{XXX}} \left({x}^{2} - {y}^{2}\right) = \left(x + y\right) \left(x - y\right)$