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

1 Answer
Dec 30, 2015

Answer:

#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#.