How will ((a+b)^3-(a^3+b^3)) be written in factor form?

Correct answer: 3ab(a+b)

The governing concept is the cube identity followed by extraction of a common factor. Expand the binomial: (a+b)^3=a^3+3a^2b+3ab^2+b^3. Now subtract a^3+b^3. The pure cube terms cancel, leaving 3a^2b+3ab^2. Both remaining terms contain 3ab, so factor it out: 3a^2b+3ab^2=3ab(a+b). Thus option A is correct. Option B has an incorrect minus sign; expanding 3ab(a-b) gives 3a^2b-3ab^2, whereas both remaining terms here are positive. Option C omits the coefficient and variables produced by the expansion. Option D is also wrong because only the pure cubes cancel; the two middle terms remain.