document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=154087>Question 154087</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Explain the following in your own words: (a + b)2  a2 + b2. Give a numerical example to illustrate this. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #113408 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=113408\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Algebraic Explanation:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28a%2Bb%29%5E2=a%5E2+%2B+b%5E2 ALIGN=MIDDLE  ALT=\"%28a%2Bb%29%5E2=a%5E2+%2B+b%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given equation\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E2%2B2ab%2Bb%5E2=a%5E2+%2B+b%5E2 ALIGN=MIDDLE  ALT=\"a%5E2%2B2ab%2Bb%5E2=a%5E2+%2B+b%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > FOIL the left side<BR>\n" );
document.write( " \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2ab=a%5E2+%2B+b%5E2-a%5E2-b%5E2 ALIGN=MIDDLE  ALT=\"2ab=a%5E2+%2B+b%5E2-a%5E2-b%5E2\"   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\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
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;\" > Combine like terms\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Case 1: Solving for \"a\"\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=0%2F%282b%29 ALIGN=MIDDLE  ALT=\"a=0%2F%282b%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2b ALIGN=MIDDLE  ALT=\"2b\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
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;\" > Reduce\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Or...\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Case 2: Solving for \"b\"\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=0%2F%282a%29 ALIGN=MIDDLE  ALT=\"b=0%2F%282a%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2b ALIGN=MIDDLE  ALT=\"2b\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<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;\" > Reduce\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "So <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28a%2Bb%29%5E2=a%5E2+%2B+b%5E2 ALIGN=MIDDLE  ALT=\"%28a%2Bb%29%5E2=a%5E2+%2B+b%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > is true only if \"a\" or \"b\" is 0 (or both are zero). Otherwise, the equation is false. So in general <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28a%2Bb%29%5E2+%3C%3E+a%5E2+%2B+b%5E2 ALIGN=MIDDLE  ALT=\"%28a%2Bb%29%5E2+%3C%3E+a%5E2+%2B+b%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Numerical Example:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28a%2Bb%29%5E2=a%5E2+%2B+b%5E2 ALIGN=MIDDLE  ALT=\"%28a%2Bb%29%5E2=a%5E2+%2B+b%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given equation\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%285%2B4%29%5E2=5%5E2%2B4%5E2 ALIGN=MIDDLE  ALT=\"%285%2B4%29%5E2=5%5E2%2B4%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in a=5 and b=4 (any two numbers will do as long as they are both not equal to zero)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%289%29%5E2=5%5E2%2B4%5E2 ALIGN=MIDDLE  ALT=\"%289%29%5E2=5%5E2%2B4%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Add\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=81=25%2B16 ALIGN=MIDDLE  ALT=\"81=25%2B16\"   DISABLED_style= \"max-width:90%; height:auto;\" > Square each term\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=81=41 ALIGN=MIDDLE  ALT=\"81=41\"   DISABLED_style= \"max-width:90%; height:auto;\" > Add\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=81=41 ALIGN=MIDDLE  ALT=\"81=41\"   DISABLED_style= \"max-width:90%; height:auto;\" > is <b>not</b> true, this means that we've just shown that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28a%2Bb%29%5E2=a%5E2+%2B+b%5E2 ALIGN=MIDDLE  ALT=\"%28a%2Bb%29%5E2=a%5E2+%2B+b%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > is <b>not</b> true for all values of \"a\" and \"b\". \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "So once again, in general <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28a%2Bb%29%5E2+%3C%3E+a%5E2+%2B+b%5E2 ALIGN=MIDDLE  ALT=\"%28a%2Bb%29%5E2+%3C%3E+a%5E2+%2B+b%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >  </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );