Published by:
CGP EDU Academic Team
Published on: August 14, 2026
Find the coefficient of x 5 in the expansion of (1 + 2x) 6 (1 – x) 7
Text Solution
Verified by ExpertsThe correct answer is:
1
Sol. (1 + 2x) 6 (1 – x) 7
= ( 6 C 0 + 6 C 1 .2x + 6 C 2 .2 2 x 2 + ...... + 6 C 6 2 6 x 6 ) × ( 7 C 0 – 7 C 1 x + 7 C 2 x 2 ........ 7 C 7 x 7 )
Coeff. of x 5 = –
6 C 0 . 7 C 5 + 6 C 1 .2. 7 C 4 – 6 C 2 .2 2 . 7 C 3 + 6 C 3 .2 3 . 7 C 2 – 6 C 4 . 2 4 . 7 C 1 + 6 C 5 .2 5 . 7 C 0
=–21+(12)(35)–(15×4)(35)+(20×8×21)–(15×16×7)+(6×32)
= – 21 + 420 – 2100 + 3360 × 1680 = 171
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