The product of two sums of squares

I just happened upon this extra nifty little fact - the set of sums of two squares is closed under multiplication.

That is, facts like (10² + 9²) × (1² + 1²) = 19² + 1² occur for every
(a² + b²) × (c² + d²).

Take a look - simple result, I am surprised I hadn't seen it before...

See the Brahmagupta-Fibonacci identity at Wikipedia