document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=44910>Question 44910</A>: <I><SPAN STYLE=\"word-break: break-all;\"> factor each polynomial completely by factoring out any common factors and then factor by grouping. Do not combine like terms.<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #29771 by </B><A HREF=/tutors/aboutme.mpl?userid=Chris435435><B>Chris435435(8)</B></A><img src=\"/images/stars/stars-05.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Chris435435><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=29771\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> I tried to factor out an a from the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3a%5E3%2B3ab%5E2 ALIGN=MIDDLE  ALT=\"3a%5E3%2B3ab%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > part of the expression<BR>\n" );
document.write( "and a b from the remaining part of the expression.  I was able to factor and a from the first expression because an a is common in each term of the expression.  That is, there is an a and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3a%5E3 ALIGN=MIDDLE  ALT=\"3a%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" > and an a in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3ab%5E2 ALIGN=MIDDLE  ALT=\"3ab%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3a%5E3 ALIGN=MIDDLE  ALT=\"3a%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3ab%5E2 ALIGN=MIDDLE  ALT=\"3ab%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > are called \"terms\" of the \"expression\" <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3a%5E3%2B3ab%5E2 ALIGN=MIDDLE  ALT=\"3a%5E3%2B3ab%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >  Because they both have an a in them, I can take an a out.  Similar reasoning with b takes place too.  Using this reasoning, I obtained the expression.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%283a%5E2%2B3b%5E2%29%2Bb%282a%5E2%2B2b%5E2%29 ALIGN=MIDDLE  ALT=\"a%283a%5E2%2B3b%5E2%29%2Bb%282a%5E2%2B2b%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now I just think of factor by grouping to be a special name for this type of factoring situation.  However, it's the same exact idea as before.  Treat <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E2%283a%2B2b%29 ALIGN=MIDDLE  ALT=\"a%5E2%283a%2B2b%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > as one term and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%282a%5E2%2B2b%5E2%29 ALIGN=MIDDLE  ALT=\"b%282a%5E2%2B2b%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > as another term of the expression <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%283a%5E2%2B3b%5E2%29+%2Bb%282a%5E2%2B2b%5E2%29 ALIGN=MIDDLE  ALT=\"a%283a%5E2%2B3b%5E2%29+%2Bb%282a%5E2%2B2b%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  Unfortunately, there isn't a common factor in either of these terms.  So we will have to try another approach.\r<BR>\n" );
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document.write( "Let's start over.  Let's try to rearrange the terms so that we can get some terms with a common factor between them.  \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3a%5E3%2B2a%5E2b%2B3ab%5E2%2B2b%5E3 ALIGN=MIDDLE  ALT=\"3a%5E3%2B2a%5E2b%2B3ab%5E2%2B2b%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" >  \r<BR>\n" );
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document.write( "Using similar reasoning to how I factored before I obtain:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E2%283a%2B2b%29%2Bb%5E2%283a%2B2b%29 ALIGN=MIDDLE  ALT=\"a%5E2%283a%2B2b%29%2Bb%5E2%283a%2B2b%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "There is a common factor between each term, that is (3a+2b) is the common factor.  Thus, using factor by grouping I obtain the factored form:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283a%2B2b%29%28a%5E2%2Bb%5E2%29 ALIGN=MIDDLE  ALT=\"%283a%2B2b%29%28a%5E2%2Bb%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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