document.write( "Question 1175216: Factor
\n" ); document.write( "ab^3 - a^3b + bc^3 - b^3c + ca^3 - c^3a. How would I go about doing this problem? Thanks! \n" ); document.write( "

Algebra.Com's Answer #800801 by ikleyn(52803) $\"\"$ $\"About$

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document.write( "I'd say \r\n" );
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document.write( "    If you are an average student and if you don't know the solution in advance, \r\n" );
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document.write( "    you will be not able to complete this assignment without help from outside\r\n" );
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document.write( "         (without help from some outer source as Wikipedia; or some advanced textbook; or some web-site).\r\n" );
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document.write( "For more advanced Algebra student, the way of thinking can be THIS:\r\n" );
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document.write( "    a)  you have a polynomial of the uniform degree 4;\r\n" );
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document.write( "        hence, you may expect having the product of four homogeneous linear binomials;\r\n" );
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document.write( "    b)  if you change \"a\" for \"b\" everywhere in the left side, left side \r\n" );
document.write( "        will change its sign.\r\n" );
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document.write( "        If you change \"a\" for \"c\" everywhere in the left side, left side \r\n" );
document.write( "        will change its sign.\r\n" );
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document.write( "        If you change \"b\" for \"c\" everywhere in the left side, left side \r\n" );
document.write( "        will change its sign.\r\n" );
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document.write( "        Hence, the advanced student can foresee that the factored form should contain the factors (a-b), (a-c) and (b-c).\r\n" );
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document.write( "        Thus such student just sees the product  (a-b)*(a-c)*(b-c)  through the fog at the horizon.\r\n" );
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document.write( "     c)  And then the student must make a super-human effort to guess that the last multiplier is (a+b+c).\r\n" );
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\n" ); document.write( "\n" ); document.write( "To get a success, such a student should be trained analyzing symmetric (or antisymmetric) \r
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\n" ); document.write( "\n" ); document.write( "For more information, see this link\r
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\n" ); document.write( "\n" ); document.write( "https://math.stackexchange.com/questions/1379045/how-to-factor-intricate-polynomial-ab3-a3b-a3c-ac3-bc3-b3c\r
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