# How do you factor 5w^3-1080?

Feb 16, 2017

$5 {w}^{3} - 1080 = 5 \left(w - 6\right) \left({w}^{2} + 6 w + 36\right)$

#### Explanation:

The difference of cubes identity can be written:

${a}^{3} - {b}^{3} = \left(a - b\right) \left({a}^{2} + a b + {b}^{2}\right)$

We can use this with $a = w$ and $b = 6$ as follows:

$5 {w}^{3} - 1080 = 5 \left({w}^{3} - 216\right)$

$\textcolor{w h i t e}{5 {w}^{3} - 1080} = 5 \left({w}^{3} - {6}^{3}\right)$

$\textcolor{w h i t e}{5 {w}^{3} - 1080} = 5 \left(w - 6\right) \left({w}^{2} + 6 w + {6}^{2}\right)$

$\textcolor{w h i t e}{5 {w}^{3} - 1080} = 5 \left(w - 6\right) \left({w}^{2} + 6 w + 36\right)$

The remaining quadratic factor has no linear factors with Real coefficients.