Brahmagupta-Fibonacci Identity

Theorem
Let $a, b, c, d$ be numbers.

Then:


 * $\paren {a^2 + b^2} \paren {c^2 + d^2} = \paren {a c + b d}^2 + \paren {a d - b c}^2$

Also known as
This identity is also known as Fibonacci's Identity.

Also see
Lagrange's Identity, of which this the case where $n = 2$.