SOLUTION: please help me with this particular problem..thanks Find the constant term or the term independent of x in the expansion of (3x-5/x^2)^9. this is a paper given as a study guid

Question 74041: please help me with this particular problem..thanks
Find the constant term or the term independent of x in the expansion of
(3x-5/x^2)^9.
this is a paper given as a study guide.thanks
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Rewrite as:
(3x - 5x^-2)^9
This is a binomial; the expansion contains 10 terms;
Look at the powers of "x" in the eqpansion
1st term has (x)^9(x^-2)^0)
2nd term has (x)^8(x^-2)^1 = x^6
3rd term has (x)^7(x^-2)^2 = x^3
4th term has (x)^6(x^-2)^3 = x^6*x^-6 = 1
So the 4th term is a "constant" term.
---------------
The complete 4th term is:
9C6*(3x)^6*(-5x^-2)^3 = 84*729x^6*-125x^-6
=-7654500
============
Cheers,
Stan H.

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