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Edit the title as seems fit.

$\begin{align} (a^3+b^3) &= (a+b)(a^2 -ab+b^2) \\ &= (a+b)^3 -3ab(a+b) \end{align}$

And so on and so forth. Right now, I only need these expansions in solving quadratic equations. But why do signs vary in the expansions? (asterisk). What controls this? I see that something similar comes in $a^2-b^2 = (a+b)(a-b)$ to allow the intermediate term(s) to cancel but how does this translate to other (higher-order) forms?

Level: US Grade-10 equivalent.

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    The way you're using words to ask this question isn't translating well. I think you may have a valid question. But, the current choice o$f$ words makes it very hard to $u$nderstand.2012-05-12

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One way of looking at this is to see that you need the intermediate terms to cancel, so taking out a factor of $(a+b)$ you will need alternating signs for the cancellation to work.

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    Thank you; the gears clicked into place! Once the exams are over, I'll put on an answer that's -hopefully- as intuitive as I get it now.2012-05-18