Question

Factorise 8p^3-q^3-12p^2q+6pq^2

Answer 1

This is a special case called the Sum of Cubes.  Here's a formula on how to solve it:  a^3 + b^3 = (a + b)(a^2 – ab + b^2)  For this problem the answer would be:  (2p + 3q)(4p^2 - 6pq + 9q^2)  Always check your answers by FOILing:  8p^3 - 12p^2q + 18pq^2 + 12p^2q - 18pq^2 + 27q^3  = 8p^3+27q^3