What is the name of this mathematical identity, 2^2 = (x+1/x)^2 - (x-1/x)^2?

Question

Can anybody please tell me if this Mathematical Identity has a name? A proper name, I have been messing around with it, and I would like to find out more information about it.

Any help appreciated.

Kind regards

Answer 1

Difference of Squares Pattern

A^2 - B^2 = (A +B)(A-b)

In this here case, A = x+1/x and B=x-1/x

A + B A - B

[(x+1/x) + (x-1/x)] [ (x+1/x) - (x-1/x) ] =

2x * 2/x <--- 1/x cancels in the first factor; x cancels in the second factor

=4x/x

= 4

=2^2