# How do you factor 3r^3-192r?

Jan 4, 2017

$3 r \left(r - 8\right) \left(r + 8\right)$

#### Explanation:

The first step is to take out a $\textcolor{b l u e}{\text{common factor}}$ of 3r

$\Rightarrow 3 r \left({r}^{2} - 64\right)$

We now have a $\textcolor{b l u e}{\text{difference of squares}}$ inside the bracket, which factorises in general as.

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

$\text{here " a = r" and } b = 8$

$\Rightarrow {r}^{2} - 64 = \left(r - 8\right) \left(r + 8\right)$

$\text{Pulling it all together gives}$

$3 {r}^{3} - 192 r = 3 r \left(r - 8\right) \left(r + 8\right)$