Question

(a+b)^3 - (a-b)^3 = ?​

Answer 1

Answer:

Expanding:

(a+b)3−(a−b)3

=(a3+3a2b+3ab2+b3)−(a3−3a2b+3ab2−b3)

=6a2b+2b3

=2b(3a2+b2)

If you are allowed complex coefficients this can be broken down into linear factors:

=2b(√3a+ib)(√3a−ib)

Notice also that:

(a+b)3+(a−b)3=(b+a)3−(b−a)3=2a(3b2+a2)