Square of Sum with Double/Algebraic Proof 2

Proof
A direct application of 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 $n = 2, x = a, y = 2 b$.