Some students might argue that if you know how to factor a sum of cubes, then you do not need to know how to factor a difference of cubes. Explain why you agree or disagree.

Answer 1

agree
if A^3 + B^3 = (A+B)(A^2 - AB + B^2)

so in A^3 - B^3
= A^3 + (-B)^3 , and now using the sum of cubes factoring
= (A + (-B) (A^2 - A(-B) + (-B)^2)
= (A-B) (A^2 + AB + B^2)