Square of Sum with Double/Algebraic Proof 2

Theorem

 * $\forall a, b \in \R: \left({a + 2 b}\right)^2 = a^2 + 4 a b + 4b^2$

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 $n = 2, x = a, y = 2b$.