# How to derive sum of cubes formula?

• Oct 31st 2005, 09:52 PM
How to derive sum of cubes formula?
How do you derive:

A^3 + B^3 = (A+B)(A^2-AB+B^2)

Thanks!
• Nov 30th 2005, 01:51 PM
CaptainBlack
Quote:

How do you derive:

A^3 + B^3 = (A+B)(A^2-AB+B^2)

Thanks!

It is obvious that

$A\ =\ -B$
is a root of

$A^3\ +\ B^3$
then synthetic division division of

$A^3\ +\ B^3$
by

$A\ +\ B$
will give the second factor on the right.

Alternativly you could just multiply out

$(A+B)(A^2-AB+B^2)$
to get

$A^3\ +\ B^3$
RonL