Binomial Theorem/Examples/4th Power of Sum

Theorem

 * $\forall x, y \in \R: \left({x + y}\right)^4 = x^4 + 4 x^3 y + 6 x^2 y^2 + 4 x y^3 + y^4$

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

putting $n = 4$.