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Find the middle term in the expansion of (x2-2x)8 - Mathematics and Statistics

Sum

Find the middle term in the expansion of `(x^2 - 2/x)^8`

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Solution

Here, a = x2, b = `(-2)/x`, n = 12

Now, n is even

∴ `("n" + 2)/2 = (8 + 2)/2` = 5

∴ Middle term is t5, for which r = 4.

We have, tr+1 = nCr an–r .br

∴ t5 = `""^8"C"_4 (x^2)^4 ((-2)/x)^4`

= `(8!)/(4!4!) (x^8)(16/x^4)`

= `(8 xx 7 xx 6 xx 5)/(4 xx 3 xx 2 xx 1) xx x^8/x^4 xx 16`

= 1120x4

∴ Middle term is 1120x4.

Concept: Middle term(s) in the 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
Exercise 4.3 | Q 4. (iii) | Page 80
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