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Question
Expand the following:
(2p + 3)(2p – 4)(2p – 5)
Solution
(2p + 3)(2p – 4)(2p – 5)
(x + a)(x + b)(x + c) ≡ x3 + (a + b + c) x2 + (ab + ba + ca) x + abc
(2p + 3)(2p – 4)(2p – 5) = (2p)3 + (3 – 4 – 5) (2p)2 + [(3 × – 4)2 + (– 4 × – 5) + (– 5 × 3)] 2p + 3 × – 4 × – 5
= 8p3 + (– 6) (4p2) + [–12 + 20 + (–15)] 2p + 60
= 8p3 – 24p2 + (–7)2p + 60
(2p + 3)(2p – 4)(2p – 5) = 8p3 – 24p2 – 14p + 60
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