document.write( "Question 1030573: find the term independent of x in the expansion of (1+x^2)(2x+1/x)^10 \n" ); document.write( "

Algebra.Com's Answer #645790 by robertb(5830) $\"\"$ $\"About$

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$\"%281%2Bx%5E2%29%282x%2B1%2Fx%29%5E10+\"$
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\n" ); document.write( "\n" ); document.write( "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 $\"C%2810%2C+6%29%2A2%5E%2810-6%29+=+C%2810%2C+6%29%2A2%5E4\"$ .\r
\n" ); document.write( "\n" ); document.write( "Therefore, the term independent of x in the expansion of $\"%281%2Bx%5E2%29%282x%2B1%2Fx%29%5E10\"$ is the constant term $\"+C%2810%2C+5%29%2A2%5E5+%2B+C%2810%2C+6%29%2A2%5E4\"$ . \n" ); document.write( "

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