# How do you factor 216u^3 - v^3?

May 24, 2016

$\left(6 u - v\right) \left(36 {u}^{2} + 6 u v + {v}^{2}\right)$

#### Explanation:

This is a $\textcolor{b l u e}{\text{difference of cubes}}$

and in general is factorised as follows.

$\textcolor{red}{| \overline{\underline{\textcolor{w h i t e}{\frac{a}{a}} \textcolor{b l a c k}{{a}^{3} - {b}^{3} = \left(a - b\right) \left({a}^{2} + a b + {b}^{2}\right)} \textcolor{w h i t e}{\frac{a}{a}} |}}}$

here $216 {u}^{3} = {\left(6 u\right)}^{3} \Rightarrow a = 6 u$

and ${v}^{3} = {\left(v\right)}^{3} \Rightarrow b = v$

$\Rightarrow 216 {u}^{3} - {v}^{3} = \left(6 u - v\right) \left(36 {u}^{2} + 6 u v + {v}^{2}\right)$