document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=458405>Question 458405</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5Em%2Aa%5En=a%5Emn ALIGN=MIDDLE  ALT=\"a%5Em%2Aa%5En=a%5Emn\"   DISABLED_style= \"max-width:90%; height:auto;\" >,then m(n-2)+n(m-2)is?options are (a)-1,(b)1 (c)0 (d)1/2 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #314465 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=314465\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Use the idea that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E%28y%29%2Ax%5E%28z%29=x%5E%28y%2Bz%29 ALIGN=MIDDLE  ALT=\"x%5E%28y%29%2Ax%5E%28z%29=x%5E%28y%2Bz%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > to state that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5Em%2Aa%5En=a%5Emn ALIGN=MIDDLE  ALT=\"a%5Em%2Aa%5En=a%5Emn\"   DISABLED_style= \"max-width:90%; height:auto;\" > is also the same as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E%28m%2Bn%29=a%5Emn ALIGN=MIDDLE  ALT=\"a%5E%28m%2Bn%29=a%5Emn\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Now, if the bases are equal, then the exponents are equal. So <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m%2Bn=mn ALIGN=MIDDLE  ALT=\"m%2Bn=mn\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=mn=m%2Bn ALIGN=MIDDLE  ALT=\"mn=m%2Bn\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Now all we need to do is start with m(n-2)+n(m-2) and simplify\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "m(n-2)+n(m-2)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "mn-2m+nm-2n \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "mn-2m+mn-2n \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "mn+mn-2m-2n \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "2mn-2(m+n)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "2(m+n)-2(m+n) .... Note: I've replaced mn with m+n (since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=mn=m%2Bn ALIGN=MIDDLE  ALT=\"mn=m%2Bn\"   DISABLED_style= \"max-width:90%; height:auto;\" >)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "0\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "So all this shows us that m(n-2)+n(m-2) = 0 when m+n = mn\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Consequently, this means that m(n-2)+n(m-2) = 0 if <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5Em%2Aa%5En=a%5Emn ALIGN=MIDDLE  ALT=\"a%5Em%2Aa%5En=a%5Emn\"   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( "So the answer is choice C) </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );