document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=40949>Question 40949</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 2x^2+2xy+x+y </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #26349 by </B><A HREF=/tutors/aboutme.mpl?userid=tutorcecilia><B>tutorcecilia(2152)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=tutorcecilia><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=tutorcecilia><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=26349\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> This problem involves factoring by grouping terms together.\r<BR>\n" );
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document.write( "The first step is to find two nice groups containing like terms so that we can factor out the GCF.  Usually there will only be two groups of terms.\r<BR>\n" );
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document.write( "Try placing parenthesis around the first two terms and the second two terms.\r<BR>\n" );
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document.write( "  (2x^2+2xy)+(x+y)\r<BR>\n" );
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document.write( "Now, look for the GCF (greatest common factor) within each group.  Sometimes you may have to switch terms within groups until they have a GFC.\r<BR>\n" );
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document.write( "Next, factor out the GCF from each group.\r<BR>\n" );
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document.write( "The first group (2x^2+2xy)has a GCF of \"2x\".  So factor out the 2x. <BR>\n" );
document.write( "This will leave:<BR>\n" );
document.write( "  (2x)(x+y) \r<BR>\n" );
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document.write( "The second group (x+y) only has a GCF of \"1\". So factor out the 1.<BR>\n" );
document.write( "This will leave:<BR>\n" );
document.write( "  (1)(x+y)\r<BR>\n" );
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document.write( "Putting everything back together gives:\r<BR>\n" );
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document.write( "  (2x)(x+y)+ (1)(x+y)\r<BR>\n" );
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document.write( "Now,again factor out the GCF from the entire expression.  What does each term have in common?  What is the GCF?\r<BR>\n" );
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document.write( "The GCF is \"(x+y)\".  So after factoring out (x+y), group the remaining terms together to get the final answer.\r<BR>\n" );
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document.write( "  (x+y)(2x+1)\r<BR>\n" );
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document.write( "Check the answer by multiplying the factors using FOIL.<BR>\n" );
document.write( "  (x+y)(2x+1)\r<BR>\n" );
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document.write( "  2x^2 + x + 2xy + y\r<BR>\n" );
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document.write( "Rearranging the terms:\r<BR>\n" );
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document.write( "  2x^2 + 2xy + x + y takes you back to the original expression.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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