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How do you factor sum or difference of two cubes and why does this process make sense?
Wiki User
∙ 13y ago
(a -b) · (a2+ab+b2) = (a3+a2b+ab2) - (a2b+ab2+b3) = a3 -b3
(a+b) · (a2 -ab+b2) = (a3 -a2b+ab2) +(a2b -ab2+b3) = a3+b3
More generally:
(a ∓ b) · (an-1 ±an-2b +an-3b2 ±an-4b3 +±...+a(±b)n-2 +(±b)n-1) = an ± bn.
The mixed terms cancel out themselves.
Wiki User
∙ 13y ago
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