document.write( "Question 174465: what is the solution for (x^5-y^5)/(x-y) \n" ); document.write( "
Algebra.Com's Answer #129459 by Edwin McCravy(20060)\"\" \"About 
You can put this solution on YOUR website!
Edwin's complete solution:\r
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document.write( "Most people learn the factorization of \"x%5EN-y%5EN%29\".\r\n" );
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document.write( "But if you forget you can divide that problem out using long division:\r\n" );
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document.write( "              x4  +  x3y  +  x2y2 +  xy3 + y4\r\n" );
document.write( "      ---------------------------------------\r\n" );
document.write( "x - y ) x5 + 0x4y + 0x3y2 + 0x2y3 + 0xy4 - y5\r\n" );
document.write( "        x5 -  x4y\r\n" );
document.write( "        ---------\r\n" );
document.write( "              x4y + 0x3y2\r\n" );
document.write( "              x4y -  x3y2\r\n" );
document.write( "              -----------\r\n" );
document.write( "                     x3y2 + 0x2y3\r\n" );
document.write( "                     x3y2 -  x2y3\r\n" );
document.write( "                     ------------\r\n" );
document.write( "                             x2y3 + 0xy4\r\n" );
document.write( "                             x2y3 -  xy4\r\n" );
document.write( "                             -----------\r\n" );
document.write( "                                     xy4 - y5\r\n" );
document.write( "                                     xy4 - y5\r\n" );
document.write( "                                     --------\r\n" );
document.write( "                                            0\r\n" );
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document.write( "So the answer is \r\n" );
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document.write( "x4  +  x3y  +  x2y2 +  xy3 + y4\r\n" );
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document.write( "However if you memorize how to factor \"x%5EN+-+y%5EN\", i.e.,\r\n" );
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document.write( "then you will know how to factor \"x%5E5-y%5E5\". Then to simplify\r\n" );
document.write( "the expression\r\n" );
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document.write( "\"%28x%5E5-y%5E5%29%2F%28x-y%29\"\r\n" );
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document.write( "you will just factor the numerator according to the rule above:\r\n" );
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document.write( "\"%28%28x-y%29%28x%5E4%2Bx%5E3y%2Bx%5E2y%5E2%2Bxy%5E3%2By%5E4%29%29%2F%28x-y%29\"\r\n" );
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document.write( "\"x%5E4%2Bx%5E3y%2Bx%5E2y%5E2%2Bxy%5E3%2By%5E4%29\".\r\n" );
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document.write( "One thing to remember though, is that although that factorization\r\n" );
document.write( "method holds for all values of N, it only factors COMPLETELY when\r\n" );
document.write( "N is an ODD positive integer.  When N is EVEN, you should always \r\n" );
document.write( "begin by factoring it as the difference of two squares.  \r\n" );
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document.write( "Edwin
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