document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=328450>Question 328450</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Explain, in your own words, the step-by-step process to simplifying the expression below. Include the simplified answer in your explanation.\r<BR>\n" );
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document.write( "(6x^2 &#8722; 5) &#8722; (3x^2 + x + 7)  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #235251 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=235251\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Garamond\" size=\"+2\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ (6x^2\ -\ 5)\ -\ (3x^2\ +\ x\ +\ 7)\">\r<BR>\n" );
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document.write( "The first thing to do is to remove parentheses. The first set of parentheses has no lead coefficient, so you can just remove them without doing anything else.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ 6x^2\ -\ 5\ -\ (3x^2\ +\ x\ +\ 7)\">\r<BR>\n" );
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document.write( "Notice that the second set of parentheses has a minus sign in front of it.  That is the same as saying there is a coefficient of -1 in front of that set of parentheses, thus:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ 6x^2\ -\ 5\ +\ (-1)(3x^2\ +\ x\ +\ 7)\">\r<BR>\n" );
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document.write( "Use the distributive property to remove this set of parentheses.  Effectively, you simply take off the parentheses and change every sign that was formerly inside of the parentheses -- including the understood + sign in front of the first term:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ 6x^2\ -\ 5\ -\ 3x^2\ -\ x\ -\ 7\">\r<BR>\n" );
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document.write( "Now you can combine like terms.  Terms with the same variable(s) AND the same exponent(s) are alike.  It is like adding up things on your kitchen table.  If you have 6 apples and 3 apples you can say you have 9 apples.  But if you have 6 apples and 3 cookies, that's all you can say:  6 apples and 3 cookies.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ 6x^2\ -\ 3x^2\ =\ 3x^2\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ -5\ -\ 7\ =\ -12\">\r<BR>\n" );
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document.write( "And there is no other term like <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large -x\">, so putting it all together:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ 3x^2\ -\ x\ -\ 12\">\r<BR>\n" );
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document.write( "And that is as simple as this one gets.\r<BR>\n" );
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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" );
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