document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=179515>Question 179515</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0321233832/algebrahomeworkh>Elementary and Intermediate Algebra Concepts and Applications</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> (a+b)^2= a^2+b^2<BR>\n" );
document.write( "Explain in the following in your own words. Give numerical example to illustrate. Please help. Thanks! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #134461 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=134461\">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=%28a%2Bb%29%5E2=+a%5E2%2Bb%5E2 ALIGN=MIDDLE  ALT=\"%28a%2Bb%29%5E2=+a%5E2%2Bb%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > is NOT true in general, here's why:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28a%2Bb%29%5E2=+a%5E2%2Bb%5E2 ALIGN=MIDDLE  ALT=\"%28a%2Bb%29%5E2=+a%5E2%2Bb%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given equation.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E2%2B2ab%2Bb%5E2=+a%5E2%2Bb%5E2 ALIGN=MIDDLE  ALT=\"a%5E2%2B2ab%2Bb%5E2=+a%5E2%2Bb%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > FOIL\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cross%28a%5E2-a%5E2%29%2B2ab%2Bcross%28b%5E2-b%5E2%29=+cross%28a%5E2-a%5E2%29%2Bcross%28b%5E2-b%5E2%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E2 ALIGN=MIDDLE  ALT=\"a%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > from both sides. 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 both sides. Notice how the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E2 ALIGN=MIDDLE  ALT=\"a%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > and the <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;\" > terms cancel out.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2ab=0 ALIGN=MIDDLE  ALT=\"2ab=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Simplify\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=0 ALIGN=MIDDLE  ALT=\"a=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=0 ALIGN=MIDDLE  ALT=\"b=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Set each individual factor equal to zero\r<BR>\n" );
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document.write( "So <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28a%2Bb%29%5E2=+a%5E2%2Bb%5E2 ALIGN=MIDDLE  ALT=\"%28a%2Bb%29%5E2=+a%5E2%2Bb%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > is only true if <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=0 ALIGN=MIDDLE  ALT=\"a=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=0 ALIGN=MIDDLE  ALT=\"b=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > (or both are zero). However, for <i>any</i> other values of \"a\" and \"b\", <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28a%2Bb%29%5E2=+a%5E2%2Bb%5E2 ALIGN=MIDDLE  ALT=\"%28a%2Bb%29%5E2=+a%5E2%2Bb%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > is NOT true.\r<BR>\n" );
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document.write( "Here's an example to support the answer:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28a%2Bb%29%5E2=+a%5E2%2Bb%5E2 ALIGN=MIDDLE  ALT=\"%28a%2Bb%29%5E2=+a%5E2%2Bb%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given equation.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282%2B3%29%5E2=2%5E2%2B3%5E2 ALIGN=MIDDLE  ALT=\"%282%2B3%29%5E2=2%5E2%2B3%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=2 ALIGN=MIDDLE  ALT=\"a=2\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=3 ALIGN=MIDDLE  ALT=\"b=3\"   DISABLED_style= \"max-width:90%; height:auto;\" > (just pick 2 random values. Make sure that both are nonzero values)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%5E2=2%5E2%2B3%5E2 ALIGN=MIDDLE  ALT=\"5%5E2=2%5E2%2B3%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Add\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%5E2=4%2B3%5E2 ALIGN=MIDDLE  ALT=\"5%5E2=4%2B3%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Square 2 to get 4\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%5E2=4%2B9 ALIGN=MIDDLE  ALT=\"5%5E2=4%2B9\"   DISABLED_style= \"max-width:90%; height:auto;\" > Square 3 to get 9\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=25=4%2B9 ALIGN=MIDDLE  ALT=\"25=4%2B9\"   DISABLED_style= \"max-width:90%; height:auto;\" > Square 5 to get 25\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=25=13 ALIGN=MIDDLE  ALT=\"25=13\"   DISABLED_style= \"max-width:90%; height:auto;\" > Add\r<BR>\n" );
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document.write( "Since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=25%3C%3E13 ALIGN=MIDDLE  ALT=\"25%3C%3E13\"   DISABLED_style= \"max-width:90%; height:auto;\" >, this means that we've just shown an example where <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28a%2Bb%29%5E2=+a%5E2%2Bb%5E2 ALIGN=MIDDLE  ALT=\"%28a%2Bb%29%5E2=+a%5E2%2Bb%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > is not true. So <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28a%2Bb%29%5E2=+a%5E2%2Bb%5E2 ALIGN=MIDDLE  ALT=\"%28a%2Bb%29%5E2=+a%5E2%2Bb%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > is not true in general </SPAN>\n" );
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