Sophie Germain's Identity

Theorem
For any two numbers $$x$$ and $$y$$:


 * $$x^4 + 4y^4 = \left({x^2 + 2y^2 + 2xy}\right) \left({x^2 + 2y^2 - 2xy}\right)$$

Proof
Multiply out the RHS:

$$ $$ $$