Brahmagupta-Fibonacci Identity

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

Then:


 * $\left({a^2 + b^2}\right) \left({c^2 + d^2}\right) = \left({a c + b d}\right)^2 + \left({a d - b c}\right)^2$

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

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