# a^2 + b^2

• February 6th 2006, 02:17 AM
phgao
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!
• February 6th 2006, 02:48 AM
jacs
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
• February 6th 2006, 03:05 AM
rgep
Quote:

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 $a^2 + b^2 = (a+ib)(a-ib)$ which quickly leads you to the fact that the product of sums of two squares is again a sum of two squares: $(a^2+b^2)(c^2+d^2) = (ac-bd)^2 + (ad+bc)^2$.
• February 6th 2006, 03:26 AM
phgao
Ah, thanks to both of you. Especially the factorization with i .