identity

**z1llch** · July 1st 2009, 06:46 AM

$a^3+b^3 = (a+b)(a^2-ab+b^2)$
why is it so?

**alexmahone** · July 1st 2009, 06:52 AM

$(a+b)(a^2-ab+b^2)=a^3-a^2b+ab^2+a^2b-ab^2+b^3=a^3+b^3$

**z1llch** · July 1st 2009, 07:02 AM

well. but if prove from left to right?

**yeongil** · July 1st 2009, 07:20 AM

Why?

If you really want to, just go backwards in this manner:

$\begin{aligned}<br /> a^3 + b^3 &= a^3 {\color{red}+ a^2b - a^2b - ab^2 + ab^2} + b^3\;\;\;\text{(adding zero)} \\<br /> &= a^2(a + b) - ab(a + b) + b^2(a + b) \\<br /> &= (a + b)(a^2 - ab + b^2)<br /> \end{aligned}$

01

Thread: identity

LinkBack

Thread Tools

Display

identity

Similar Math Help Forum Discussions

the i*pi=ln(-1) identity

identity

Identity

An identity

identity

Search Tags