Binomial Theorem/Examples/4th Power of Difference

Example of Use of Binomial Theorem

 * $\paren {x - y}^4 = x^4 - 4 x^3 y + 6 x^2 y^2 - 4 x y^3 + y^4$

Proof
Follows directly from the Binomial Theorem:
 * $\displaystyle \forall n \in \Z_{\ge 0}: \paren {x + \paren {-y} }^n = \sum_{k \mathop = 0}^n \binom n k x^{n - k} \paren {-y}^k$

putting $n = 4$.