Brahmagupta-Fibonacci Identity/Proof 2

Proof
From the more general version of Brahmagupta-Fibonacci Identity:
 * $\left({a^2 + n b^2}\right) \left({c^2 + n d^2}\right) = \left({a c + n b d}\right)^2 + n \left({a d - b c}\right)^2$

The result follows by setting $n = 1$.