Q2 of 59 Page 7

Find the expansion of

(3x + 1)(3x + 2)(3x + 5)

(3x + 1)(3x + 2)((3x + 5)


Here we have to use the identity


(x + a)(x + b)(x + c) = x3 + (a + b + c)x2 + (ab + bc + ca)x + abc


∴ (3x + 1)(3x + 2)((3x + 5)


= (3x)3 + (1 + 2 + 5)(3x)2 + (1 × 2 + 2 × 5 + 5 × 1)(3x) + 1 × 2 × 5


= 27 x3 + (8)9x2 + (2 + 10 + 5) (3x) + 1 × 2 × 5


= 27 x3 + 72x2 + 51x + 10


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