# Expansion of (x-(3/x^2)^9

#### acc

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!

#### mr fantastic

MHF Hall of Fame
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!
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.