document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=376644>Question 376644</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I need help solving a problem that I was told to use the cubic special product pattern.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p%5E3%2B6p%5E2q%2B12pq%5E2%2B8q%5E3 ALIGN=MIDDLE  ALT=\"p%5E3%2B6p%5E2q%2B12pq%5E2%2B8q%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "I started by using grouping, but I really am not sure what the cubic special product pattern is. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #267947 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=267947\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> This problem is a bit tricky as you're going to use multiple factoring methods (and a bit of creativity).\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p%5E3%2B6p%5E2q%2B12pq%5E2%2B8q%5E3 ALIGN=MIDDLE  ALT=\"p%5E3%2B6p%5E2q%2B12pq%5E2%2B8q%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given expression.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p%5E3%2B8q%5E3%2B6p%5E2q%2B12pq%5E2 ALIGN=MIDDLE  ALT=\"p%5E3%2B8q%5E3%2B6p%5E2q%2B12pq%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Rearrange the terms where the cubic terms are the first two terms.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28p%2B2q%29%28p%5E2-2pq%2B4q%5E2%29%2B6pq%28p%2B2q%29 ALIGN=MIDDLE  ALT=\"%28p%2B2q%29%28p%5E2-2pq%2B4q%5E2%29%2B6pq%28p%2B2q%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Factor <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p%5E3%2B8q%5E3 ALIGN=MIDDLE  ALT=\"p%5E3%2B8q%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" > using the sum of cubes formula and factor out the GCF <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6pq ALIGN=MIDDLE  ALT=\"6pq\"   DISABLED_style= \"max-width:90%; height:auto;\" > from the last two terms.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28p%2B2q%29%28p%5E2-2pq%2B4q%5E2%2B6pq%29 ALIGN=MIDDLE  ALT=\"%28p%2B2q%29%28p%5E2-2pq%2B4q%5E2%2B6pq%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Now factor out the GCF <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p%2B2q ALIGN=MIDDLE  ALT=\"p%2B2q\"   DISABLED_style= \"max-width:90%; height:auto;\" > from the entire expression.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28p%2B2q%29%28p%5E2%2B4pq%2B4q%5E2%29 ALIGN=MIDDLE  ALT=\"%28p%2B2q%29%28p%5E2%2B4pq%2B4q%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28p%2B2q%29%28p%2B2q%29%28p%2B2q%29 ALIGN=MIDDLE  ALT=\"%28p%2B2q%29%28p%2B2q%29%28p%2B2q%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Factor <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p%5E2%2B4pq%2B4q%5E2 ALIGN=MIDDLE  ALT=\"p%5E2%2B4pq%2B4q%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28p%2B2q%29%28p%2B2q%29 ALIGN=MIDDLE  ALT=\"%28p%2B2q%29%28p%2B2q%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28p%2B2q%29%5E3 ALIGN=MIDDLE  ALT=\"%28p%2B2q%29%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" > Condense the factors.\r<BR>\n" );
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document.write( "So <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p%5E3%2B6p%5E2q%2B12pq%5E2%2B8q%5E3 ALIGN=MIDDLE  ALT=\"p%5E3%2B6p%5E2q%2B12pq%5E2%2B8q%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" > completely factors to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28p%2B2q%29%5E3 ALIGN=MIDDLE  ALT=\"%28p%2B2q%29%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "In other words, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p%5E3%2B6p%5E2q%2B12pq%5E2%2B8q%5E3=%28p%2B2q%29%5E3 ALIGN=MIDDLE  ALT=\"p%5E3%2B6p%5E2q%2B12pq%5E2%2B8q%5E3=%28p%2B2q%29%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "If you need more help, email me at <a  rel=nofollow HREF=\"mailto:jim_thompson5910@hotmail.com?Subject=Algebra%20Help\">jim_thompson5910@hotmail.com</a>\r<BR>\n" );
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document.write( "Also, feel free to check out my <a  rel=nofollow HREF=\"http://www.freewebs.com/jimthompson5910/home.html\">tutoring website</a>\r<BR>\n" );
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document.write( "Jim </SPAN>\n" );
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