document.write( "Question 1117568: find the term independent of x in the expansion of {2x^3 - 1/4(x^5)}^8 \n" ); document.write( "

Algebra.Com's Answer #733017 by ikleyn(52781) $\"\"$ $\"About$

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\n" ); document.write( "\n" ); document.write( " The correct answer is -28.\r
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\n" ); document.write( "\n" ); document.write( " See the full and correct solution below.\r
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document.write( "The binomial expansion is this formula\r\n" );
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document.write( " =  +  +  +  + . . . +  + \r\n" );
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document.write( "In our case,  n = 8,  a = ,  b = -,  therefore, the binomial expansion in our case is  \r\n" );
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document.write( " =  +  +  +  + . . . +  + .\r\n" );
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document.write( "The general term of this expansion is   =  = .\r\n" );
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document.write( "The term independent of x is at  3*(8-k) - 5k = 0,  or\r\n" );
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document.write( "    24 - 3k - 5k = 0  ====>  24 = 8k  ====>  k = 3   (the fourth term).\r\n" );
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document.write( "Then the coefficient at this term is   =  =  = -28.\r\n" );
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\n" ); document.write( "\n" ); document.write( "The solution by @greenestamps giving the answer \"28\" contains an error.\r
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