# How do you factor the difference of two perfect squares: (x+7)^2-25?

Nov 22, 2016

${\left(x + 7\right)}^{2} - 25 = \left(x + 2\right) \left(x + 12\right)$

#### Explanation:

The difference of squares identity can be written:

${a}^{2} - {b}^{2} = \left(a - b\right) \left(a + b\right)$

Hence we find:

${\left(x + 7\right)}^{2} - 25 = {\left(x + 7\right)}^{2} - {5}^{2}$

$\textcolor{w h i t e}{{\left(x + 7\right)}^{2} - 25} = \left(\left(x + 7\right) - 5\right) \left(\left(x + 7\right) + 5\right)$

$\textcolor{w h i t e}{{\left(x + 7\right)}^{2} - 25} = \left(x + 2\right) \left(x + 12\right)$