Question

find the coefficient of 1/x^3 in the expansion of (3x-2/x^2)^6

Answer 1

The expansion of (a+b)^6 has the coefficients

1 6 15 20 15 6 1
and 1/x^3 equals x^3*(1/x^2)^3=1/x^3
So it's the middle term:
20[(3x)^3(-2/x^2)^3]
Multiply them all out to find the coefficient.