Maharashtra State BoardHSC Science (General) 11th
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Answer the following: Find third term in the expansion of (9x2-y36)4 - Mathematics and Statistics

Sum

Answer the following:

Find third term in the expansion of `(9x^2 - y^3/6)^4`

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Solution

Here a = 9x2, b = `(-y^3)/6`, n = 4

For 3rd term, r = 2

We have, tr+1 = nCr an–r .br

∴ t3 = `""^4"C"_2 (9x^2)^(4 - 2)((-y^3)/6)^2`

= `(4!)/(2!2!)(81x^4).y^6/36`

= `(4 xx 3)/(2 xx 1) xx 81x^4 xx y^6/36`

= `27/2 x^4y^6`

∴ 3rd term in the expansion of `(9x^2 - y^3/6)^4` is `27/2 x^4y^6`.

Concept: General Term in Expansion of (a + b)n
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APPEARS IN

Balbharati Mathematics and Statistics 2 (Arts and Science) 11th Standard Maharashtra State Board
Chapter 4 Methods of Induction and Binomial Theorem
Miscellaneous Exercise 4 | Q II. (6) | Page 85
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