# How do you factor m^3 - n^3?

Dec 30, 2015

${m}^{3} - {n}^{3} = \left(m - n\right) \left({m}^{2} + m n + {n}^{2}\right)$

#### Explanation:

This is a standard identity known as the "difference of cubes" identity.

The remaining quadratic factor can only be factored further using Complex coefficients:

$\left({m}^{2} + m n + {n}^{2}\right) = \left(m - \omega n\right) \left(m - {\omega}^{2} n\right)$

where $\omega = - \frac{1}{2} + \frac{\sqrt{3}}{2} i$ is the primitive Complex cube root of $1$.