# How do you factor 2x^3-18x?

Dec 4, 2016

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

#### Explanation:

Separate out the common factor $2 x$, then use the difference of squares identity:

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

with $a = x$ and $b = 3$ as follows:

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

$\textcolor{w h i t e}{2 {x}^{3} - 18 x} = 2 x \left({x}^{2} - {3}^{2}\right)$

$\textcolor{w h i t e}{2 {x}^{3} - 18 x} = 2 x \left(x - 3\right) \left(x + 3\right)$