# How do you factor 2p^3-162p?

Apr 15, 2017

$2 p \left(p - 9\right) \left(p + 9\right)$

#### Explanation:

The first step is to take out the $\textcolor{b l u e}{\text{common factor}}$ of 2p

rArr2p(p^2-81)tocolor(red)((1)

$\text{ the factor " (p^2-81)" is a " color(blue)"difference of squares}$

$\text{and factorises, in general as}$

$\textcolor{red}{\overline{\underline{| \textcolor{w h i t e}{\frac{2}{2}} \textcolor{b l a c k}{{a}^{2} - {b}^{2} = \left(a - b\right) \left(a + b\right)} \textcolor{w h i t e}{\frac{2}{2}} |}}}$

$\text{here " a=p" and } b = 9$

$\Rightarrow {p}^{2} - 81 = \left(p - 9\right) \left(p + 9\right)$

$\text{returning to } \textcolor{red}{\left(1\right)}$

$\Rightarrow 2 {p}^{3} - 162 p = 2 p \left(p - 9\right) \left(p + 9\right)$