Brahmagupta-Fibonacci Identity/General

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


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