SOLUTION: find the term independent of x in the expansion of (1+x^2)(2x+1/x)^10

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Question 1030573: find the term independent of x in the expansion of (1+x^2)(2x+1/x)^10
Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
%281%2Bx%5E2%29%282x%2B1%2Fx%29%5E10+
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In the first sum in the last expression, the term that is independent of x is when k = 5, i.e., C%2810%2C+5%29%2A2%5E%2810-5%29+=+C%2810%2C+5%29%2A2%5E5, while in the 2nd sum, is the term C%2810%2C+6%29%2A2%5E%2810-6%29+=+C%2810%2C+6%29%2A2%5E4.
Therefore, the term independent of x in the expansion of %281%2Bx%5E2%29%282x%2B1%2Fx%29%5E10 is the constant term +C%2810%2C+5%29%2A2%5E5+%2B+C%2810%2C+6%29%2A2%5E4.