SOLUTION: Find the term in x^4 in the expansion of (3x^2-2/x)^5

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Question 1150515: Find the term in x^4 in the expansion of (3x^2-2/x)^5
Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!
The general term of 

%28A%2BB%29%5EN 

is 

%22C%28N%2Ck%29%22A%5E%28N-k%29B%5Ek 

So the general term of 

%283x%5E2-2%2Fx%29%5E5 

is 

%22C%285%2Ck%29%22%283x%5E2%29%5E%285-k%29%28-2%2Fx%29%5Ek 

Which we simplify:

%22C%285%2Ck%29%223%5E%285-k%29x%5E%282%285-k%29%29expr%28%28-2%29%5Ek%2Fx%5Ek%29%29 


%22C%285%2Ck%29%22%28-2%29%5Ek%2A3%5E%285-k%29expr%28x%5E%2810-2k%29%2Fx%5Ek%29

We subtract exponents of x

%22C%285%2Ck%29%22%28-2%29%5Ek%2A3%5E%285-k%29x%5E%2810-3k%29

Since we want the term in x4, we set the exponent of x
equal to 4

10-3k = 4
  -3k = -6
    k = 2

So we substitute 2 for k

%22C%285%2C2%29%22%28-2%29%5E2%2A3%5E%285-2%29x%5E%2810-3%2A2%29

10%284%29%2A3%5E%283%29x%5E%2810-6%29

10%284%29%2A27x%5E4

1080x%5E4

Edwin