# How do you factor (x+5)^2 - 81?

May 11, 2015

${\left(x + 5\right)}^{2} - 81$
is the same as ${\left(x + 5\right)}^{2} - {9}^{2}$

Any expression of the form ${a}^{2} - {b}^{2}$ can be factored as
${a}^{2} - {b}^{2} = \left(a + b\right) \left(a - b\right)$

For the given example $a = \left(x + 5\right)$ and $b = 9$

So
${\left(x + 5\right)}^{2} - 81 = \left(\left(x + 5\right) + 9\right) \left(x + 5 - 9\right)$
which simplifies as
$\left(x + 14\right) \left(x - 4\right)$