document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=107879>Question 107879</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/9780073268620/algebrahomeworkh></A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> I'm having a hard time understanding the AC method.  I have the following problem that has to be solved using the AC method, and I'm lost.  Please help.\r<BR>\n" );
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document.write( "6m^6n+7m^5n^2+2m^4n^3 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #78637 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=78637\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Take the first coefficient (6) and the last coefficient (2) and multiply them to get 12. Now what two numbers multiply to 12 but add to the middle coefficient of 7?\r<BR>\n" );
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document.write( "It turns out that 4 and 3 multiply to 12 and add to 7.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6m%5E6n%2B4m%5E5n%5E2%2B3m%5E5n%5E2%2B2m%5E4n%5E3 ALIGN=MIDDLE  ALT=\"6m%5E6n%2B4m%5E5n%5E2%2B3m%5E5n%5E2%2B2m%5E4n%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" > Now replace the middle term <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7m%5E5n%5E2 ALIGN=MIDDLE  ALT=\"7m%5E5n%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > with the sum <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4m%5E5n%5E2%2B3m%5E5n%5E2 ALIGN=MIDDLE  ALT=\"4m%5E5n%5E2%2B3m%5E5n%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > (these two are equivalent)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%286m%5E6n%2B4m%5E5n%5E2%29%2B%283m%5E5n%5E2%2B2m%5E4n%5E3%29 ALIGN=MIDDLE  ALT=\"%286m%5E6n%2B4m%5E5n%5E2%29%2B%283m%5E5n%5E2%2B2m%5E4n%5E3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Group like terms\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2m%5E5n%283m%2B2n%29%2B%283m%5E5n%5E2%2B2m%5E4n%5E3%29 ALIGN=MIDDLE  ALT=\"2m%5E5n%283m%2B2n%29%2B%283m%5E5n%5E2%2B2m%5E4n%5E3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Factor out the GCF <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2m%5E5n ALIGN=MIDDLE  ALT=\"2m%5E5n\"   DISABLED_style= \"max-width:90%; height:auto;\" > out of the first group\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2m%5E5n%283m%2B2n%29%2Bm%5E4n%5E2%283m%2B2n%29 ALIGN=MIDDLE  ALT=\"2m%5E5n%283m%2B2n%29%2Bm%5E4n%5E2%283m%2B2n%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Factor out the GCF <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m%5E4n%5E2 ALIGN=MIDDLE  ALT=\"m%5E4n%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > out of the second group\r<BR>\n" );
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document.write( "Notice we have a common term of 3m+2n, this means we can combine like terms\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282m%5E5n%2Bm%5E4n%5E2%29%283m%2B2n%29 ALIGN=MIDDLE  ALT=\"%282m%5E5n%2Bm%5E4n%5E2%29%283m%2B2n%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms\r<BR>\n" );
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document.write( "Notice how <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282m%5E5n%2Bm%5E4n%5E2%29%283m%2B2n%29 ALIGN=MIDDLE  ALT=\"%282m%5E5n%2Bm%5E4n%5E2%29%283m%2B2n%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >  foils to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6m%5E6n%2B4m%5E5n%5E2%2B3m%5E5n%5E2%2B2m%5E4n%5E3 ALIGN=MIDDLE  ALT=\"6m%5E6n%2B4m%5E5n%5E2%2B3m%5E5n%5E2%2B2m%5E4n%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" >, so this verifies our answer.\r<BR>\n" );
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