In the expansion of (x-(3/x^2)^9 find the following:

a) the term containing x6

b) the constant term

This is my last question, I swear! :P

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- May 12th 2010, 11:08 AMaccExpansion of (x-(3/x^2)^9
In the expansion of (x-(3/x^2)^9 find the following:

a) the term containing x6

b) the constant term

This is my last question, I swear! :P - May 12th 2010, 08:53 PMmr fantastic
The general term is $\displaystyle {9 \choose r} x^{9 - r} \left( -\frac{3}{x^2}\right)^r = {9 \choose r} (-3)^r x^{9 - r} x^{-2r} = {9 \choose r} (-3)^r x^{9 - 3r}$.

a) You require the coefficient of the power of x corresponding to 9 - 3r = 6.

b) You require the coefficient of the power of x corresponding to 9 - 3r = 0.