Binomial Theorem/Examples/5th Power of Sum

Example of Use of Binomial Theorem

 * $\paren {x + y}^5 = x^5 + 5 x^4 y + 10 x^3 y^2 + 10 x^2 y^3 + 5 x y^4 + y^5$

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

putting $n = 5$.