Difference of Two Squares

Theorem
Let $\struct {R, +, \circ}$ be a commutative ring whose zero is $0_R$.

Let $x, y \in R$.

Then:
 * $x \circ x + \paren {- \paren {y \circ y} } = \paren {x + y} \circ \paren {x + \paren {-y} }$

When $R$ is one of the standard sets of numbers, that is $\Z, \Q, \R$, and so on, then this translates into:
 * $x^2 - y^2 = \paren {x + y} \paren {x - y}$