Question

Factorise the following:
(p² + p)² - 8(p² + p) + 12

Answer 1

(p² + p)² - 8(p² + p) + 12
= (p² + p)² - 6(p² + p) - 2(p² + p) + 12
= (p² + p)(p² + p - 6) - 2(p² + p - 6)
= (p² + p - 6)(p² + p - 2)
= (p² + 3p - 2p - 6)(p² + 2p - p - 2)
= [p(p + 3) - 2(p + 3)][p(p + 2) - 1(p + 2)]
= [(p + 3)(p - 2)][(p + 2)(p - 1)]
= (p + 3)(p - 2)(p + 2)(p - 1).