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Example 7 - Find coefficient of x6y3 in expansion (x + 2y)^9

Example  7 - Chapter 8 Class 11 Binomial Theorem - Part 2

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Example 7 Find the coefficient of x6y3 in the expansion of (x + 2y)9. We know that General term of expansion (a + b)n is Tr+1 = nCr an–r br For (x + 2y)9, Putting n = 9 , a = x , b = 2y Tr + 1 = 9Cr (x)9 – r (2y)r = 9Cr (x)9 – r . (y)r . (2)r We need to find coefficient of x6 y3 Comparing yr = y3 r = 3 Putting r = 3 in (1) T3+1 = 9C3 x9 – 3 . y3 . (2)3 = 9!/3!(9 −3 )! x6 . y3 . (2)3 = 9!/(3! 6!) (2)3 x6 y3 = (9 × 8 × 7 × 6!)/(3 × 2 × 1 × 6!) × 8 . x6 y3 = (9 × 8 × 7 × 8 )/(3 × 2) x6 y3 = 672 x6 y3 Hence coefficient of x6 y3 is 672

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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.