Square of Sum less Square/Algebraic Proof 1

Theorem

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

Proof

Follows directly and trivially from Square of Sum:

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

\(=\)

\(\ds x^2 + 2 x y + y^2\)

Square of Sum

\(\ds \leadsto \ \ \)

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

\(=\)

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

$\blacksquare$