document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=150454>Question 150454</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Perform the indicated operation\r<BR>\n" );
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document.write( "(2b +3)(5b-1)-(b + 2)^2  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #110409 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=110409\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282b+%2B3%29%285b-1%29-%28b+%2B+2%29%5E2 ALIGN=MIDDLE  ALT=\"%282b+%2B3%29%285b-1%29-%28b+%2B+2%29%5E2\"   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=%2810b%5E2%2B13b-3%29-%28b+%2B+2%29%5E2 ALIGN=MIDDLE  ALT=\"%2810b%5E2%2B13b-3%29-%28b+%2B+2%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > FOIL <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282b+%2B3%29%285b-1%29 ALIGN=MIDDLE  ALT=\"%282b+%2B3%29%285b-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282b+%2B3%29%285b-1%29=10b%5E2-2b%2B15b-3=10b%5E2%2B13b-3 ALIGN=MIDDLE  ALT=\"%282b+%2B3%29%285b-1%29=10b%5E2-2b%2B15b-3=10b%5E2%2B13b-3\"   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=%2810b%5E2%2B13b-3%29-%28b+%2B+2%29%28b+%2B+2%29 ALIGN=MIDDLE  ALT=\"%2810b%5E2%2B13b-3%29-%28b+%2B+2%29%28b+%2B+2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Expand <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28b+%2B+2%29%5E2 ALIGN=MIDDLE  ALT=\"%28b+%2B+2%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28b+%2B+2%29%28b+%2B+2%29 ALIGN=MIDDLE  ALT=\"%28b+%2B+2%29%28b+%2B+2%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=%2810b%5E2%2B13b-3%29-%28b%5E2%2B4b%2B4%29 ALIGN=MIDDLE  ALT=\"%2810b%5E2%2B13b-3%29-%28b%5E2%2B4b%2B4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > FOIL <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28b+%2B+2%29%28b+%2B+2%29 ALIGN=MIDDLE  ALT=\"%28b+%2B+2%29%28b+%2B+2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28b+%2B+2%29%28b+%2B+2%29=b%5E2%2B2b%2B2b%2B4=b%5E2%2B4b%2B4 ALIGN=MIDDLE  ALT=\"%28b+%2B+2%29%28b+%2B+2%29=b%5E2%2B2b%2B2b%2B4=b%5E2%2B4b%2B4\"   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=10b%5E2%2B13b-3-b%5E2-4b-4%29 ALIGN=MIDDLE  ALT=\"10b%5E2%2B13b-3-b%5E2-4b-4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Distribute the negative. Think of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-%28b%5E2%2B4b%2B4%29 ALIGN=MIDDLE  ALT=\"-%28b%5E2%2B4b%2B4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1%28b%5E2%2B4b%2B4%29 ALIGN=MIDDLE  ALT=\"-1%28b%5E2%2B4b%2B4%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=%2810b%5E2-b%5E2%29%2B%2813b-4b%29%2B%28-3-4%29 ALIGN=MIDDLE  ALT=\"%2810b%5E2-b%5E2%29%2B%2813b-4b%29%2B%28-3-4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Group like terms. Make sure that each group is separated by a \"+\" sign.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%289b%5E2%29%2B%2813b-4b%29%2B%28-3-4%29 ALIGN=MIDDLE  ALT=\"%289b%5E2%29%2B%2813b-4b%29%2B%28-3-4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2 ALIGN=MIDDLE  ALT=\"b%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > from <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10b%5E2 ALIGN=MIDDLE  ALT=\"10b%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9b%5E2 ALIGN=MIDDLE  ALT=\"9b%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=%289b%5E2%29%2B%289b%29%2B%28-3-4%29 ALIGN=MIDDLE  ALT=\"%289b%5E2%29%2B%289b%29%2B%28-3-4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4b ALIGN=MIDDLE  ALT=\"4b\"   DISABLED_style= \"max-width:90%; height:auto;\" > from <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=13b ALIGN=MIDDLE  ALT=\"13b\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9b ALIGN=MIDDLE  ALT=\"9b\"   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=%289b%5E2%29%2B%289b%29%2B%28-7%29 ALIGN=MIDDLE  ALT=\"%289b%5E2%29%2B%289b%29%2B%28-7%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4 ALIGN=MIDDLE  ALT=\"4\"   DISABLED_style= \"max-width:90%; height:auto;\" > from <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3 ALIGN=MIDDLE  ALT=\"-3\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-7 ALIGN=MIDDLE  ALT=\"-7\"   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=9b%5E2%2B9b-7 ALIGN=MIDDLE  ALT=\"9b%5E2%2B9b-7\"   DISABLED_style= \"max-width:90%; height:auto;\" > Remove the parenthesis.\r<BR>\n" );
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document.write( "Answer:\r<BR>\n" );
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document.write( "So <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282b+%2B3%29%285b-1%29-%28b+%2B+2%29%5E2 ALIGN=MIDDLE  ALT=\"%282b+%2B3%29%285b-1%29-%28b+%2B+2%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > simplifies to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9b%5E2%2B9b-7 ALIGN=MIDDLE  ALT=\"9b%5E2%2B9b-7\"   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=%282b+%2B3%29%285b-1%29-%28b+%2B+2%29%5E2=9b%5E2%2B9b-7 ALIGN=MIDDLE  ALT=\"%282b+%2B3%29%285b-1%29-%28b+%2B+2%29%5E2=9b%5E2%2B9b-7\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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