Brahmagupta-Fibonacci Identity/General/Corollary

Corollary to General Version of Brahmagupta-Fibonacci Identity
Let $a, b, c, d, n$ be numbers.

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