Posted by **steve** on Tuesday, May 24, 2011 at 10:43pm.

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

A. 10th

B. 11th

C. 12th

D. 13th

- math -
**MathMate**, Wednesday, May 25, 2011 at 12:17am
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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