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Question
Find the constant term (term independent of x) in the expansion of `(x - 2/x^2)^15`
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Solution
Here, a = x, b = `(-2)/x^2`, n = 15
We have, tr+1 = nCr an–r .br
= `""^15"C"_"r" (x)^(15 - "r")*((-2)/x^2)^"r"`
= 15Cr x15–r.(–2)r. x–2r
= 15Cr (–2)r x15–3r
To get the term independent of x, we must have
x15–3r = x0
∴ 15 – 3r = 0
∴ r = 5
∴ the term independent of x
= 15C5 (– 2)5
= `(15!)/(5!10!)(-2)^5`
= `(15 xx 14 xx 13 xx 12 xx 11)/(5 xx 4 xx 3 xx 2 xx 1) xx (-32)`
= – 96096
∴ the term independent of x is – 96096.
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