document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=190672>Question 190672</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0321233832/algebrahomeworkh></A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> Using FOIL, multiply the expression (3x+2)(3x-2) Show that a particular factoring formula can be used to get the same answer.  Thanks so much! I'm lost again! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #143147 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=143147\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283x%2B2%29%283x-2%29 ALIGN=MIDDLE  ALT=\"%283x%2B2%29%283x-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given expression.\r<BR>\n" );
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document.write( "Now let's FOIL the expression.\r<BR>\n" );
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document.write( "Remember, when you FOIL an expression, you follow this procedure:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28highlight%283x%29%2B2%29%28highlight%283x%29-2%29 ALIGN=MIDDLE  ALT=\"%28highlight%283x%29%2B2%29%28highlight%283x%29-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply the <font color=\"red\">F</font>irst terms:<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283%2Ax%29%2A%283%2Ax%29=9%2Ax%5E2 ALIGN=MIDDLE  ALT=\"%283%2Ax%29%2A%283%2Ax%29=9%2Ax%5E2\"   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=%28highlight%283x%29%2B2%29%283x%2Bhighlight%28-2%29%29 ALIGN=MIDDLE  ALT=\"%28highlight%283x%29%2B2%29%283x%2Bhighlight%28-2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply the <font color=\"red\">O</font>uter terms:<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283%2Ax%29%2A%28-2%29=-6%2Ax ALIGN=MIDDLE  ALT=\"%283%2Ax%29%2A%28-2%29=-6%2Ax\"   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=%283x%2Bhighlight%282%29%29%28highlight%283x%29-2%29 ALIGN=MIDDLE  ALT=\"%283x%2Bhighlight%282%29%29%28highlight%283x%29-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply the <font color=\"red\">I</font>nner terms:<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282%29%2A%283%2Ax%29=6%2Ax ALIGN=MIDDLE  ALT=\"%282%29%2A%283%2Ax%29=6%2Ax\"   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=%283x%2Bhighlight%282%29%29%283x%2Bhighlight%28-2%29%29 ALIGN=MIDDLE  ALT=\"%283x%2Bhighlight%282%29%29%283x%2Bhighlight%28-2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply the <font color=\"red\">L</font>ast terms:<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282%29%2A%28-2%29=-4 ALIGN=MIDDLE  ALT=\"%282%29%2A%28-2%29=-4\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "---------------------------------------------------\r<BR>\n" );
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document.write( "So we have the terms: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9%2Ax%5E2 ALIGN=MIDDLE  ALT=\"9%2Ax%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-6%2Ax ALIGN=MIDDLE  ALT=\"-6%2Ax\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6%2Ax ALIGN=MIDDLE  ALT=\"6%2Ax\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4 ALIGN=MIDDLE  ALT=\"-4\"   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=9%2Ax%5E2-6%2Ax%2B6%2Ax-4 ALIGN=MIDDLE  ALT=\"9%2Ax%5E2-6%2Ax%2B6%2Ax-4\"   DISABLED_style= \"max-width:90%; height:auto;\" > Now add every term listed above to make a single expression.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9%2Ax%5E2-4 ALIGN=MIDDLE  ALT=\"9%2Ax%5E2-4\"   DISABLED_style= \"max-width:90%; height:auto;\" > Now combine like terms.\r<BR>\n" );
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document.write( "So <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283x%2B2%29%283x-2%29 ALIGN=MIDDLE  ALT=\"%283x%2B2%29%283x-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > FOILs to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9%2Ax%5E2-4 ALIGN=MIDDLE  ALT=\"9%2Ax%5E2-4\"   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=%283x%2B2%29%283x-2%29=9x%5E2-4 ALIGN=MIDDLE  ALT=\"%283x%2B2%29%283x-2%29=9x%5E2-4\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "Now, let's factor the answer to check our work:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9x%5E2-4 ALIGN=MIDDLE  ALT=\"9x%5E2-4\"   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=%283x%29%5E2-4 ALIGN=MIDDLE  ALT=\"%283x%29%5E2-4\"   DISABLED_style= \"max-width:90%; height:auto;\" > Rewrite <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9x%5E2 ALIGN=MIDDLE  ALT=\"9x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283x%29%5E2 ALIGN=MIDDLE  ALT=\"%283x%29%5E2\"   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=%283x%29%5E2-%282%29%5E2 ALIGN=MIDDLE  ALT=\"%283x%29%5E2-%282%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Rewrite <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4 ALIGN=MIDDLE  ALT=\"4\"   DISABLED_style= \"max-width:90%; height:auto;\" > as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282%29%5E2 ALIGN=MIDDLE  ALT=\"%282%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "Notice how we have a difference of squares <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%5E2-B%5E2 ALIGN=MIDDLE  ALT=\"A%5E2-B%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > where in this case <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=3x ALIGN=MIDDLE  ALT=\"A=3x\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=B=2 ALIGN=MIDDLE  ALT=\"B=2\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "So let's use the difference of squares formula <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%5E2-B%5E2=%28A%2BB%29%28A-B%29 ALIGN=MIDDLE  ALT=\"A%5E2-B%5E2=%28A%2BB%29%28A-B%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > to factor the expression:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%5E2-B%5E2=%28A%2BB%29%28A-B%29 ALIGN=MIDDLE  ALT=\"A%5E2-B%5E2=%28A%2BB%29%28A-B%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the difference of squares formula.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283x%29%5E2-%282%29%5E2=%283x%2B2%29%283x-2%29 ALIGN=MIDDLE  ALT=\"%283x%29%5E2-%282%29%5E2=%283x%2B2%29%283x-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=3x ALIGN=MIDDLE  ALT=\"A=3x\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=B=2 ALIGN=MIDDLE  ALT=\"B=2\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "So this shows us that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9x%5E2-4 ALIGN=MIDDLE  ALT=\"9x%5E2-4\"   DISABLED_style= \"max-width:90%; height:auto;\" > factors to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283x%2B2%29%283x-2%29 ALIGN=MIDDLE  ALT=\"%283x%2B2%29%283x-2%29\"   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=9x%5E2-4=%283x%2B2%29%283x-2%29 ALIGN=MIDDLE  ALT=\"9x%5E2-4=%283x%2B2%29%283x-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "So this confirms our answer </SPAN>\n" );
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