Difference of Two Powers/Examples/Difference of Two Cubes

Theorem

 * $x^3 - y^3 = \left({x + y}\right) \left({x^2 + x y + y^2}\right)$

Proof
From Difference of Two Powers:
 * $\displaystyle a^n - b^n = \left({a - b}\right) \sum_{j \mathop = 0}^{n - 1} a^{n - j - 1} b^j$

The result follows directly by setting $n = 3$.