Published by:
CGP EDU Academic Team
Published on: August 14, 2026
(i) Find the coefficient of x 12 in 
(ii) Find the coefficient of x 100 in 
Text Solution
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(i) 142
(ii) – 197
(i) (4 + 2x – x 2 ) (1 + x) –3
= 4 × coeff of x 12 + 2 × coeff of x 11 – 1 × coeff of x 10
In (1 + x) –3
T r+1 = (–1) r 3+r–1 C r x r
= (–1) r r+2 C r x r
= 4 × 14 C 12 – 2 × 13 C 11 – 12 C 10
= 
= 364 – 156 – 66 = 142
(ii) (3 – 5x) (1 – x) –2
= 3 × coeff of x 100 – 5 × coeff of x 99
In (1 – x) –2
T r+1 = 2+r–1 C r x r = r+1 C r x r = 3 × 101 C 100 – 5 x 100 C 99 = 3 × 101 – 5 x 100 = – 197
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