# How do you factor 4b^2 - 9?

Nov 14, 2015

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

#### Explanation:

The difference of squares formula states that
${a}^{2} - {b}^{2} = \left(a + b\right) \left(a - b\right)$
(this may be easily verified by expanding the right hand side of the equation)

$4 {b}^{2} = {\left(2 b\right)}^{2}$
$9 = {3}^{2}$

Thus, by the difference of squares formula:

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