Binomial Thm.

Degree of each term of (x-2/x^2)^3:
3,0,-3,-6
Degree of each term of (3x+1/x)^4:
4,2,0,-2,-4

Therefore it is trivial that there is only 1 constant term in the expansion of(x-2/x^2)^3(3x+1/x)^4:
3 * [x^2 * (-2/x^2)] * 6 * [(3x)^2 * (1/x)^2]
=3 * -2x^2/x^2 * 6 * 9x^2/x^2
=3 * -2 * 6 * 9
=-324

2013-06-16 08:24:37 補充：
Feel free to ask me for further questions.

Find the constant term in the expansion :
(x－2/x^2)^3(3x+1/x)^4
Sol
(x－2/x^2)^3(3x+1/x)^4
=(x^3－2)^3(3x^2+1)^4/x^10
10=6+4
C(3，2)*(－2)*C(4，2)*3^2
=3*(－2)*6*9
=－324