document.write( "Question 1013237: In the expansion of (2+x)^14 multiplied by (1+2/x)^14, find the coefficient of x^12. \n" ); document.write( "

Algebra.Com's Answer #629519 by ikleyn(52781) $\"\"$ $\"About$

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\n" ); document.write( "In the expansion of (2+x)^14 multiplied by (1+2/x)^14, find the coefficient of x^12.
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document.write( "Apply the binomial formula to expand  and . You will have \r\n" );
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document.write( " =  * .\r\n" );
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document.write( "where  are the binomial coefficients. (See the lessons \r\n" );
document.write( "  Introduction to Combinations  and \r\n" );
document.write( "  Binomial Theorem, Binomial Formula, Binomial Coefficients and Binomial Expansion \r\n" );
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document.write( "in this site).\r\n" );
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document.write( "Now, when you open parentheses, cross-multiply the terms as it is required and collect the common terms, \r\n" );
document.write( "you will see that  comes from these and only from these terms:\r\n" );
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document.write( " *  + \r\n" );
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document.write( "+  *  +\r\n" );
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document.write( "+  * .\r\n" );
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document.write( "Thus the coefficient at  will be\r\n" );
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document.write( " *  +  *  +  * .\r\n" );
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document.write( "Next substitute here   = 1,   = 1,   = 1, calculate the rest of binomial coefficients and get the answer. \r\n" );
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document.write( "My part is to give you the general idea and the pivotal direction.\r\n" );
document.write( "The rest is on you.\r\n" );
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