Brahmagupta-Fibonacci Identity/Extension/Proof 1

Proof
From the extension to the general Brahmagupta-Fibonacci Identity:
 * $\displaystyle \prod_{j \mathop = 1}^n \left({ {a_j}^2 + m {b_j}^2}\right) = c^2 + m d^2$

for some $c, d \in \Z$, for all $m \in \Z$.

The result follows by setting $m = 1$.