# Ex 8.2,8 - Chapter 8 Class 11 Binomial Theorem

Last updated at Dec. 24, 2019 by Teachoo

Last updated at Dec. 24, 2019 by Teachoo

Transcript

Ex 8.2,8 Find the middle terms in the expansions of 3 +9 10 Number of terms n = 10 Since n is even. There will be one middle term Middle term = 2 + 1 = 10 2 + 1 = 5 + 1 = 6th term. Hence we need to find 6th term. i.e. T6 We know that general term of (a + b)n is Tr+1 = nCr (a)n-r . (b)r 6th term = T6 = T5+1 of expansion 3 +9 10 Hence r = 5 & n = 5 , a = 3 & b = 9y T5 + 1 = 10C5 3 10 5 . (9y)5 T6 = 10C5 3 5 . (9)5 . y5 = 10! 5! 10 5 ! . 3 5 . (3)2 5 . y5 = 10! 5!5! . 5 35 . 310 . y5 = 10 9 8 7 6 5! 5 4 3 2 1 5! . x5 . 310 35 . y5 = 10 9 8 7 6 5 4 3 2 1 . x5 . 35 . y5 = 10 9 8 7 6 35 5 4 3 2 1 . x5 . y5 = 61236 x5 y5 Hence middle term of 3 +9 10 is 61236 x5 y5

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Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 9 years. He provides courses for Maths and Science at Teachoo.