SOLUTION: find the coefficient of x of the expansion (sqrt(x)-3/sqrt(x))^8

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Question 1104786: find the coefficient of x of the expansion (sqrt(x)-3/sqrt(x))^8
Answer by greenestamps(13209) About Me  (Show Source):
You can put this solution on YOUR website!


The expression is %28sqrt%28x%29-3%2Fsqrt%28x%29%29%5E8

The x term in the expansion will be obtained when the first term is used 2 more times than the second term: %28sqrt%28x%29%29%5E5%2A%281%2Fsqrt%28x%29%29%5E3+=+x%5E%285%2F2-3%2F2%29+=+x

So the binomial formula tells us the coefficient is

C%288%2C3%29%2A%28%281%29%5E5%29%2A%28%28-3%29%5E3%29+=+56%281%29%28-27%29+=+-1512