# Example 15 - Chapter 8 Class 11 Binomial Theorem

Last updated at May 29, 2018 by Teachoo

Last updated at May 29, 2018 by Teachoo

Transcript

Example 15 Find the term independent of x in the expansion of 3𝑥 + 12 3𝑥18, x > 0. Step1 : Calculate general term of expansion 3𝑥 + 12 3𝑥18 We know that general term of expansion (a + b)n is Tr+1 = nCr (a)n–r . (a)n For general term of expansion 3𝑥 + 12 3𝑥18 Putting n = 18 , a = 3𝑥 , b = 12 3𝑥 ∴ Tr+1 = 18Cr (3𝑥)18 – r 12 3𝑥𝑟 = 18Cr (𝑥)13 × (18−𝑟) 12× 13𝑥𝑟 = 18Cr (𝑥)18 − 𝑟3 12𝑟13𝑥𝑟 = 18Cr (𝑥)18 − 𝑟3 12𝑟1𝑥13𝑟 = 18Cr (𝑥)18 − 𝑟3 12𝑟 1𝑥𝑟3 = 18Cr (𝑥)18 − 𝑟3 12𝑟 𝑥−𝑟3 = 18Cr (𝑥)18 − 𝑟3 𝑥−𝑟3 12𝑟 = 18Cr (𝑥)18 − 𝑟3 − 𝑟3 12𝑟 = 18Cr (𝑥)18 − 𝑟 − 𝑟3 12𝑟 = 18Cr (𝑥)18 − 2𝑟3 12𝑟 ∴ Tr+1 = 18Cr (𝑥)18 − 2𝑟3 12𝑟 Step 2 We need to find the term independent of x So, power of x is 0 𝑥18 −2𝑟3 = x0 Comparing power 18 − 2𝑟3 = 0 18 – 2r = 0 18 = 2r 182 = r 9 = r r = 9 Putting r = 9 in (1) Tr+1 = 18Cr (𝑥)18 − 2𝑟3 12𝑟 T9+1 = 18C9 .𝑥18 −3(9)3. 129 = 18C9 .x0. 129 = 18C9 . 129 Hence, the term which is independent of x is T10 = 18C9 . 129

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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.