# How do you factor 32 - 18x^2?

Oct 1, 2015

First separate out the common scalar factor $2$, then use the difference of squares identity to find:

$32 - 18 {x}^{2} = 2 \left(4 - 3 x\right) \left(4 + 3 x\right)$

#### Explanation:

The difference of squares identity is: ${a}^{2} - {b}^{2} = \left(a - b\right) \left(a + b\right)$

Using $a = 4$ and $b = 3 x$, we find:

$32 - 18 {x}^{2} = 2 \left(16 - 9 {x}^{2}\right) = 2 \left({4}^{2} - {\left(3 x\right)}^{2}\right) = 2 \left(4 - 3 x\right) \left(4 + 3 x\right)$