# Math Help - identity

1. ## identity

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

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

3. well. but if prove from left to right?

4. Why? If you really want to, just go backwards in this manner:

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

01