Factorize!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

Question

a - b - a^3 + b^3

Answer 1

Given equation is a - b + b^3 - a^3

This can be rearranged as a - b - (a^3 - b^3)

To factorise we can use the cubic rule of (a^3 - b^3) = (a - b)(a^2 +ab + b^2)

Therefore  a - b - (a^3 - b^3) = (a - b) - (a - b)(b^2 + ab + a^2)

                                                   = (a - b)[ 1 - b^2 - ab -a^2]

                                                   = - (a - b)[ - 1 + b^2 + ab + a^2]