Question

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

Answer 1

`m^3-n^3 = (m-n)(m^2+mn+n^2)`

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:

`(m^2+mn+n^2) = (m- omega n)(m - omega^2 n)`

where `omega = -1/2+sqrt(3)/2 i` is the primitive Complex cube root of `1`.