Thread: a^2 + b^2

Is there anything you can do to a^2 + b^2 i.e can you factorise it somehow or is it only a^2 - b^2 you can factorise?

Thanks!

a² - b² = (a - b)(a + b) the difference of two squares

one way of manipulating a² + b² which comes in handy for some applications (especally in parametrics) is this


a² + b² = (a + b)² - 2ab

Originally Posted by phgao

Is there anything you can do to a^2 + b^2 i.e can you factorise it somehow or is it only a^2 - b^2 you can factorise?

It can be written as which quickly leads you to the fact that the product of sums of two squares is again a sum of two squares: .

Ah, thanks to both of you. Especially the factorization with i .