document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1039700>Question 1039700</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Simplify each of the following expressions: <BR>\n" );
document.write( "Tricky ones\r<BR>\n" );
document.write( "\n" );
document.write( "(t^1/2-2^3/2)(t^1/2+2^3/2)\r<BR>\n" );
document.write( "\n" );
document.write( "(t square root 1/2 minus 2 square root 3/2)(t square root 1/2 plus 2 square root 3/2)\r<BR>\n" );
document.write( "\n" );
document.write( "Thank you </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #654437 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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/cgi-bin/show-face.mpl?user=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=654437\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Times New Roman\" size=\"+2\">\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "First you say symbolically:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \left(t^{\frac{1}{2}}\ -\ 2^{\frac{3}{2}}\right)\left(t^{\frac{1}{2}}\ +\ 2^{\frac{3}{2}}\right)\">\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "And then you write:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \left(t\sqrt{\frac{1}{2}}\ -\ 2\sqrt{\frac{3}{2}}\right)\left(t\sqrt{\frac{1}{2}}\ +\ 2\sqrt{\frac{3}{2}}\right)\">\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Two vastly different things.  Furthermore, you don't actually ask a question, tell us what you want, or tell us what it is that you are having difficulty understanding.  It is really rather unfair of you to make us guess what you want.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "But since I have to guess, I'll guess that you meant the first expression and that you want to find the product of the two binomials.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Note that <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large a^{\frac{m}{n}}\ =\ \sqrt[n]{a^m}\"> so <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large 2^{\frac{3}{2}}\ =\ \sqrt{8}\"> and <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large t^{\frac{1}{2}}\ =\ \sqrt{t}\">\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "So you actually have:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \left(\sqrt{t}\ -\ \sqrt{8}\right)\left(\sqrt{t}\ +\ \sqrt{8}\right)\">\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "which is the product of a pair of binomial conjugates that results in the difference of two squares; recall <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large (a\ -\ b)(a\ +\ b)\ =\ a^2\ -\ b^2\">\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "John<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE e^{i\pi}\ +\ 1\ =\ 0\"><BR>\n" );
document.write( "My calculator said it, I believe it, that settles it<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" src=\"http://c0rk.blogs.com/gr0undzer0/darwin-fish.jpg\"><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \ \\r\"> </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );