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(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.

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