document.write( "Question 1185340: Find the coefficient of x^27 in the expansion of (x^2+3x)^15 \n" ); document.write( "
Algebra.Com's Answer #816161 by Edwin McCravy(20060)\"\" \"About 
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document.write( "Every term of \"%28a%2Bb%29%5En\" is of the form \"%28matrix%282%2C1%2Cn%2Cr%29%29a%5Er%2Ab%5E%28n-r%29\"\r\n" );
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document.write( "Therefore, every term of \"%28x%5E2%2B3x%29%5E15\" is of the form\r\n" );
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document.write( "\"%28matrix%282%2C1%2C15%2Cr%29%29%28x%5E2%29%5Er%2A%283x%29%5E%2815-r%29\"\r\n" );
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document.write( "\"%28matrix%282%2C1%2C15%2Cr%29%29x%5E%282r%29%2A3%5E%2815-r%29%2Ax%5E%2815-r%29\"\r\n" );
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document.write( "\"%28matrix%282%2C1%2C15%2Cr%29%29%2A3%5E%2815-r%29x%5E%2815%2Br%29\"\r\n" );
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document.write( "We want the exponent of x to be 27, so we set\r\n" );
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document.write( "15+r = 27\r\n" );
document.write( "   r = 12\r\n" );
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document.write( "\"%28matrix%282%2C1%2C15%2C12%29%29%2A3%5E%2815-12%29x%5E%2815%2B12%29\"\r\n" );
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document.write( "\"455%2A3%5E%283%29x%5E%2827%29\"\r\n" );
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document.write( "\"455%2A27x%5E%2827%29\"\r\n" );
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document.write( "\"12285x%5E%2827%29\"\r\n" );
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document.write( "Its coefficient is 12285\r\n" );
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document.write( "Edwin

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