document.write( "Question 171588: Please find the middle term in the expansion of
\n" ); document.write( "(x/3 + 9y)^10 \n" ); document.write( "
Algebra.Com's Answer #126751 by nerdybill(7384)\"\" \"About 
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\n" ); document.write( "You will need to apply the \"binomial theorem\"
\n" ); document.write( "See this site for a review:
\n" ); document.write( "http://www.purplemath.com/modules/binomial.htm
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\n" ); document.write( "The nth term is:
\n" ); document.write( "C(n,k)a^(n-k)b^k
\n" ); document.write( "where
\n" ); document.write( "C(n,k) = n!/(n-k)!k!
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\n" ); document.write( "In this case,
\n" ); document.write( "k = 4 (desired term minus 1)
\n" ); document.write( "n = 10
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\n" ); document.write( "therefore,
\n" ); document.write( "C(10,4)a^(10-4)b^4
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\n" ); document.write( "C(n,k) = n!/(n-k)!k!
\n" ); document.write( "C(10,4) = 10!/(10-4)!4!
\n" ); document.write( "C(10,4) = 10!/6!4!
\n" ); document.write( "C(10,4) = (7*8*9*10)/(1*2*3*4) = 120960
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\n" ); document.write( "So,
\n" ); document.write( "C(10,4)a^(10-4)b^4
\n" ); document.write( "120960a^6b^4
\n" ); document.write( "120960(x/3)^6(9y)^4
\n" ); document.write( "120960(x^6/729)(9y)^4
\n" ); document.write( "165.9259(x^6)(6561y^4)
\n" ); document.write( "1088640x^6y^4\r
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