document.write( "Question 1117630: the coefficient of x^2 in the expansion of (2x+k)^6 is equal to the coefficient of x^5 in the expansion of (2+kx)^8. find k \n" ); document.write( "

Algebra.Com's Answer #732926 by greenestamps(13200) $\"\"$ $\"About$

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\n" ); document.write( "The coefficient of the x^2 term in $\"%282x%2Bk%29%5E6\"$ is $\"C%286%2C2%29%2A%282%5E2%29%2A%28k%5E4%29\"$

\n" ); document.write( "The coefficient of the x^5 term in $\"%282%2Bkx%29%5E8\"$ is $\"C%288%2C5%29%2A%28k%5E5%29%2A%282%5E3%29\"$

\n" ); document.write( " $\"C%286%2C2%29%2A%282%5E2%29%2A%28k%5E4%29+=+C%288%2C5%29%2A%28k%5E5%29%2A%282%5E3%29\"$

\n" ); document.write( " $\"15%2A4%2Ak%5E4+=+56%2A8%2Ak%5E5\"$
\n" ); document.write( " $\"60k%5E4+=+448k%5E5\"$
\n" ); document.write( " $\"k+=+60%2F448+=+15%2F112\"$

\n" ); document.write( "When I got this \"ugly\" answer, I guessed that there was an error in your statement of the problem. However, wolframalpha.com confirmed that this value of k does indeed make the two coefficients equal. \n" ); document.write( "

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