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