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which term in the expansion of (1/(3x^2)-x)^15 is the constant term?

A. 10th
B. 11th
C. 12th
D. 13th

• math -

The constant term is the term where the power of x in the product (1/(3x²))^r*x^(15-r) is zero, i.e.
(x^(-2))^r*x^(15-r)=x^0
=>
-2r+(15-r)=0
r=5
In general, a polynomial in x is written in descending order of the power of x.
So the powers of x for the expansion are:
x^0*(x^(-2))^15 = x^(-30)
...
x^10*(x^(-2))^5 = x^0
...
x^12*(x^(-2))^3 = x^6
x^13*(x^(-2))^2 = x^9
x^14*(x^(-2))^1 = x^12
x^15*(x^(-2))^0 = x^15

Can you figure out which term gives the constant term?

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