Difference of Two Fifth Powers

Theorem

 * $x^5 - y^5 = \paren {x - y} \paren {x^4 + x^3 y + x^2 y^2 + x y^3 + y^4}$

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

The result follows directly by setting $n = 5$.