# identity

• July 1st 2009, 06:46 AM
z1llch
identity
$a^3+b^3 = (a+b)(a^2-ab+b^2)$
why is it so?
• July 1st 2009, 06:52 AM
alexmahone
$(a+b)(a^2-ab+b^2)=a^3-a^2b+ab^2+a^2b-ab^2+b^3=a^3+b^3$
• July 1st 2009, 07:02 AM
z1llch
well. but if prove from left to right?
• July 1st 2009, 07:20 AM
yeongil
Why? :confused: 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}

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