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

  1. Chapter 8 Class 11 Binomial Theorem
  2. Serial order wise
Ask Download

Transcript

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

About the Author

Davneet Singh's photo - Teacher, Computer Engineer, Marketer
Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 7 years. He provides courses for Mathematics and Science from Class 6 to 12. You can learn personally from here https://www.teachoo.com/premium/maths-and-science-classes/.
Jail