# How do you factor the expression (x+3)^2 - 4?

Dec 20, 2015

Use difference of squares identity to find:

${\left(x + 3\right)}^{2} - 4 = \left(x + 1\right) \left(x + 5\right)$

#### Explanation:

The difference of squares identity can be written:

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

Use this with $a = \left(x + 3\right)$ and $b = 2$ as follows:

${\left(x + 3\right)}^{2} - 4$

$= {\left(x + 3\right)}^{2} - {2}^{2}$

$= \left(\left(x + 3\right) - 2\right) \left(\left(x + 3\right) + 2\right)$

$= \left(x + 1\right) \left(x + 5\right)$