Example 7 - Find coefficient of x6y3 in (x + 2y)9 - Class 11 - General Term - Defination

  1. Chapter 8 Class 11 Binomial Theorem
  2. Serial order wise
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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 is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 8 years. He provides courses for Maths and Science at Teachoo. You can check his NCERT Solutions from Class 6 to 12.