document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1089262>Question 1089262</A>: <I><SPAN STYLE=\"word-break: break-all;\"> factor by grouping <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E3%2By%5E3-x%5E2y-xy%5E2 ALIGN=MIDDLE  ALT=\"x%5E3%2By%5E3-x%5E2y-xy%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #703599 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=703599\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> i think this would be factored as follows.\r<BR>\n" );
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document.write( "start with x^3 + y^3 - x^2y - xy^2\r<BR>\n" );
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document.write( "rearrange by descending order of degree of x.\r<BR>\n" );
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document.write( "you get:\r<BR>\n" );
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document.write( "x^3 - x^2y - xy^2 + y^3\r<BR>\n" );
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document.write( "group as shown below:\r<BR>\n" );
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document.write( "(x^3 - x^2y) - (xy^2 - y^3)\r<BR>\n" );
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document.write( "on the left group, factor out x^2.\r<BR>\n" );
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document.write( "on the right group, factor out y^2.\r<BR>\n" );
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document.write( "you will get:\r<BR>\n" );
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document.write( "x^2 * (x - y) - y^2 * (x - y)\r<BR>\n" );
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document.write( "factor out the common term of (x - y) and you get:\r<BR>\n" );
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document.write( "(x^2 - y^2) * (x - y)\r<BR>\n" );
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document.write( "(x^2 - y^2) is equal to (x - y) * (x + y)\r<BR>\n" );
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document.write( "your final factored expression becomes:\r<BR>\n" );
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document.write( "(x - y) * (x + y) * (x - y)\r<BR>\n" );
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document.write( "this expression should be equivalent to x^3 + y^3 - x^2y - xy^2\r<BR>\n" );
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document.write( "to see if it is, pick a random value for x and y and see if both expressions give you the same result.\r<BR>\n" );
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document.write( "i'll pick x = 2 and y = 3.\r<BR>\n" );
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document.write( "x^3 + y^3 - x^2y - xy^2 is equal to 5\r<BR>\n" );
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document.write( "(x-y) * (x+y) * (x-y) is equal to 5 as well.\r<BR>\n" );
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document.write( "it looks like these expressions are equivalent.\r<BR>\n" );
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document.write( "this is reasonable proof that the factorization was correct.\r<BR>\n" );
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document.write( "you can try it with other random values of x and y and you should see that the expressions are equivalent.\r<BR>\n" );
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document.write( "i redid the experiment with x = 7 and y = 4\r<BR>\n" );
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document.write( "i got 99 using each expression.\r<BR>\n" );
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document.write( "that solidifies the impression that the factorization was done correctly.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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