# How do you factor z^3 - 125?

Jan 24, 2017

$\left(z - 5\right) \left({z}^{2} + 5 z + 25\right)$

#### Explanation:

This is a $\textcolor{b l u e}{\text{difference of cubes}}$ and factorises, in general, as shown.

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

$\text{here " (z)^3=z^3" and } {\left(5\right)}^{3} = 125$

$\Rightarrow a = z \text{ and } b = 5$

$\Rightarrow {z}^{3} - 125 = \left(z - 5\right) \left({z}^{2} + 5 z + 25\right)$