document.write( "Question 1181279: Find the coefficient of x^6 in the expansion of (2x-3)^9
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Algebra.Com's Answer #811153 by ikleyn(52796)\"\" \"About 
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document.write( "The binomial expansion is this formula\r\n" );
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document.write( "    \"%28a%2Bb%29%5En\" = \"a%5En\" + \"C%5Bn%5D%5E1%2Aa%5E%28n-1%29%2Ab\" + \"C%5Bn%5D%5E2%2Aa%5E%28n-2%29%2Ab%5E2\" + \"C%5Bn%5D%5E3%2Aa%5E%28n-3%29%2Ab%5E3\" + . . . + \"C%5Bn%5D%5E%28n-1%29%2Aa%5E1%2Ab%5E%28n-1%29\" + \"b%5En\"\r\n" );
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document.write( "In our case,  n = 9,  a = 2x,  b = -3.  Therefore, the general term of the binomial expansion in our case is  \r\n" );
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document.write( "    \"C%5B9%5D%5Ek%2A%282x%29%5E%289-k%29%2A%28-3%29%5Ek\", k = 0, 1, 2, 3, 4, 5, . . . \r\n" );
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document.write( "Then the term with  x^6  is the fourth term of the expansion at k = 3 \r\n" );
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document.write( "    \"C%5B9%5D%5E3%2A%282x%29%5E%289-3%29%2A%28-3%29%5E3\" = \"%28%289%2A8%2A7%29%2F%281%2A2%2A3%29%29%2A2%5E6%2Ax%5E6%2A%28-3%29%5E3\" = \"-145162%2Ax%5E6\".    ANSWER\r\n" );
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\n" ); document.write( "\n" ); document.write( "If you want to see other similar solved problems and to learn the subject wider and deeper,  then look into the lesson\r
\n" ); document.write( "\n" ); document.write( "    - Solved problems on binomial coefficients \r
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\n" ); document.write( "\n" ); document.write( "Also, you have this free of charge online textbook in ALGEBRA-II in this site\r
\n" ); document.write( "\n" ); document.write( "    - ALGEBRA-II - YOUR ONLINE TEXTBOOK.\r
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\n" ); document.write( "\n" ); document.write( "The referred lesson is the part of this textbook under the topic
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\n" ); document.write( "\n" ); document.write( "Save the link to this textbook together with its description\r
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\n" ); document.write( "\n" ); document.write( "Free of charge online textbook in ALGEBRA-II
\n" ); document.write( "https://www.algebra.com/algebra/homework/complex/ALGEBRA-II-YOUR-ONLINE-TEXTBOOK.lesson\r
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\n" ); document.write( "\n" ); document.write( "into your archive and use when it is needed.\r
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