# How do you factor 4q^2 - 49?

Apr 21, 2016

$4 {q}^{2} - 49 = \left(2 q - 7\right) \left(2 q + 7\right)$

#### Explanation:

The difference of squares identity can be written:

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

In our example, both $4 {q}^{2} = {\left(2 q\right)}^{2}$ and $49 = {7}^{2}$ are perfect squares. So the difference of squares identity works immediately with $a = 2 q$ and $b = 7$ as follows:

$4 {q}^{2} - 49 = {\left(2 q\right)}^{2} - {7}^{2} = \left(2 q - 7\right) \left(2 q + 7\right)$