Brahmagupta - Fibonacci Identity

                                                      Brahmagupta - Fibonacci Identity 

There is a very famous identity used in algebra known as – Brahmagupta – Fibonacci identity that expresses the product of two sums of two squares as a sum of two squares in two different ways.

                        (a² + b²) (c² + d²) = (ac – bd)² + (ad + bc)²      

                                                  = ( ac + bd)² + (ad – bc)²

For example:-

(1² + 4²) (2² + 7²) = (2 – 28)² + (7 + 8)²

                            = 26² + 15²

And

(1² + 4²) (2² + 7²) = (2 + 28)² + (7 – 8)²

                            = 30² + 1²

^{Dr Rajesh Kumar Thakur}