Ex 8.2, 2 - Find coefficient of a5b7 in (a - 2b)12 - Binomial

Ex 8.2, 2 - Chapter 8 Class 11 Binomial Theorem - Part 2

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Question 2 Find the coefficient of a5b7 in (a – 2b)12 We know that general term of expansion (a + b)n Tr+1 = nCr (a)n–r . br For general term of expansion (a – 2b )12 Putting n = 12 , a = a , b = –2b Tr+1 = 12Cr (a)12 – r . (–2b)r = 12Cr (a)12 – r . (-2)r . (b)r = 12Cr (–2)r (a)12 – r. (b)r We need to find coefficient of a5b7 So b7 = b r Comparing powers 7 = r r = 7 Putting r = 7 in (1) T7+1 = 12C7 (–2)7 . (a)12 -7 . (b)7 = – 12!/(7!(12−7)!) . (-2)7 . a5 . b7 = – 12!/(7! 5!) . 27 . a5 . b7 = – (12 × 11 × 10 × 9 × 8 × 7!)/(5 × 4 × 3 × 2 × 7!) × 27 × a5 b7 = –101376 a5 b7 Hence coefficient of a5 b7 is –101376

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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science and Computer Science at Teachoo