Brahmagupta-Fibonacci Identity/Proof 2

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

The result follows by setting $n = 1$.