Brahmagupta-Fibonacci Identity/General/Corollary

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

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