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Question
Find the constant term (term independent of x) in the expansion of `(x^2 - 1/x)^9`
Solution
Here, a = x2, b = `(-1)/x`, n = 9
We have, tr+1 = nCr an–r .br
= `""^9"C"_"r" (x^2)^(9 - "r") ((-1)/x)^"r"`
= 9Cr x18–2r (–1)r .x–r
= 9Cr (–1)r x18–3r
To get the term independent of x, we must have
x18–3r = x0
∴ 18 – 3r = 0
∴ r = 6
∴ the term independent of x = 9C6 (–1)6
= `(9!)/(6!3!) xx 1`
= `(9 xx 8 xx 7)/(3 xx 2 xx 1)`
= 84
∴ the term independent of x is 84.
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