SOLUTION: In the expansion of (x^3 - 2/x^2 ) ^10, find the term in x^10, find the coefficient of 1/x^5, find the term independent of x.

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Question 1185962: In the expansion of (x^3 - 2/x^2 ) ^10, find the term in x^10, find the coefficient of 1/x^5, find the term independent of x.
Found 2 solutions by greenestamps, ikleyn:
Answer by greenestamps(13215) About Me  (Show Source):
You can put this solution on YOUR website!


(1) x^10:



(2) 1/x^5:



(3) constant term:

Answer by ikleyn(52913) About Me  (Show Source):
You can put this solution on YOUR website!
.


            I came to fix the errors in the @greenestamps' solution.


(1)   x^10:

C%2810%2C6%29%28%28x%5E3%29%5E6%29%28%28-2%2Fx%5E2%29%5E4%29 = C%2810%2C6%29%28%28-2%29%5E4%29%28x%5E18%29%281%2Fx%5E8%29 = C%2810%2C6%29%2A16%2Ax%5E10 = 3360%2Ax%5E10.


(2)   1/x^5:

C%2810%2C3%29%28%28x%5E3%29%5E3%29%28%28-2%2Fx%5E2%29%5E7%29 = C%2810%2C3%29%2A%28-2%29%5E7%2A%28x%5E9%29%281%2Fx%5E14%29 = -C%2810%2C3%29%2A128%29%2A%281%2Fx%29%5E5 = 15360%2A%281%2Fx%5E5%29


(3)   constant term:

C%2810%2C4%29%2A%28x%5E3%29%5E4%2A%28-2%2Fx%5E2%29%5E6 = C%2810%2C4%29%2A%28-2%29%5E6%29%2Ax%5E12%2A%281%2Fx%5E12%29 = C%2810%2C4%29%2A64 = 13440.


Solved.