Find the coefficient of the x^2 term in the expansion of (3x - (2/x^2))^8

Answer 1

I would advice to take out the 1/x^2 term first:

(3x - (2/x^2))^8 =

1/x^16 (3 x^3 - 2)^8 =

So you need to get x^18 from the expansion of the bracket:

(3 x^3 - 2)^8 contains a term:

(3 x^3)^6 (-2)^2 Binomial(8,6)

So, the coefficient is 81648.