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प्रश्न
Find the middle term in the expansion of `(x^2 - 2/x)^8`
उत्तर
Here, a = x2, b = `(-2)/x`, n = 8
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.
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