Binomial Theorem/Examples/6th Power of Sum

Example of Use of Binomial Theorem

 * $\paren {x + y}^6 = x^6 + 6 x^5 y + 15 x^4 y^2 + 20 x^3 y^3 + 15 x^2 y^4 + 6 x y^5 + y^6$

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 $n = 6$.