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Math Help - identity

  1. #1
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    identity

    a^3+b^3 = (a+b)(a^2-ab+b^2)
    why is it so?
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  2. #2
    MHF Contributor alexmahone's Avatar
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    (a+b)(a^2-ab+b^2)=a^3-a^2b+ab^2+a^2b-ab^2+b^3=a^3+b^3
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  3. #3
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    well. but if prove from left to right?
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  4. #4
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    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}


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