Square of Sum less Square/Algebraic Proof 2

Theorem

$\forall x, y \in \R: \paren {2x + y} y = \paren {x + y}^2 - x^2$

Proof

\(\ds \paren {x + y}^2 - x^2\)

\(=\)

\(\ds \paren {x + y + x} \paren {x + y - x}\)

Difference of Two Squares

\(\ds \)

\(=\)

\(\ds \paren {2 x + y} y\)

$\blacksquare$