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Question
Expand the following:
(3a + 1)(3a – 2)(3a + 4)
Solution
(3a + 1)(3a – 2)(3a + 4)
(x + a)(x + b)(x + c) ≡ x3 + (a + b + c) x2 + (ab + bc + ca) x + abc
(3a + 1)(3a – 2)(3a + 4) = (3a)3 + (1 – 2 + 4)(3a)2 + [1 × (– 2) + (– 2 × 4) + 4 × 1] (3a) + 1 × – 2 × 4
= 27a3 + 3(9a2) + (– 2 – 8 + 4) 3a – 8
= 27a3 + 27a2 – 8a – 8
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