document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=117895>Question 117895</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I hope I am posting this in the correct place. I am really stuck on this and do not know what to do. Please help me understand how to do this, Thank you so much.<BR>\n" );
document.write( "2{[3(m-5)+18]-[3(5m-3)+4]} </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #85877 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=85877\">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=2%28%283%28m-5%29%2B18%29-%283%285m-3%29%2B4%29%29 ALIGN=MIDDLE  ALT=\"2%28%283%28m-5%29%2B18%29-%283%285m-3%29%2B4%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "This is just an exercise in the application of the Distributive, Associative, and Commutative Properties:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Distributive Property: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%28b+%2Bc%29=ab%2Bac ALIGN=MIDDLE  ALT=\"a%28b+%2Bc%29=ab%2Bac\"   DISABLED_style= \"max-width:90%; height:auto;\" > for all real a, b, and c.<BR>\n" );
document.write( "Associative Property: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28a%2Bb%29%2Bc=a%2B%28b%2Bc%29 ALIGN=MIDDLE  ALT=\"%28a%2Bb%29%2Bc=a%2B%28b%2Bc%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > for all real a, b, and c.<BR>\n" );
document.write( "Commutative Property: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%2Bb=b%2Ba ALIGN=MIDDLE  ALT=\"a%2Bb=b%2Ba\"   DISABLED_style= \"max-width:90%; height:auto;\" > for all real a and b.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "For this problem you need to work from the inside and go out.  Start with the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%28m-5%29 ALIGN=MIDDLE  ALT=\"3%28m-5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > part.  Using the distributive property, you can write that as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3m-15 ALIGN=MIDDLE  ALT=\"3m-15\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  Same thing for the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%285m-3%29 ALIGN=MIDDLE  ALT=\"3%285m-3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > part, which can be written as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=15m-9 ALIGN=MIDDLE  ALT=\"15m-9\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  Put these two expressions back into the original expression:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%28%283m-15%29%2B18-%2815m-9%29%2B4%29%29 ALIGN=MIDDLE  ALT=\"2%28%283m-15%29%2B18-%2815m-9%29%2B4%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Now remove the parentheses around <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-%2815m-9%29 ALIGN=MIDDLE  ALT=\"-%2815m-9%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > by distributing the minus sign.  Think of the minus sign in front of a set of parentheses as a -1, and then apply the distributive property.  You end up with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-15m%2B9 ALIGN=MIDDLE  ALT=\"-15m%2B9\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  Put this back into the expression.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%28%283m-15%29%2B18-15m%2B9%2B4%29 ALIGN=MIDDLE  ALT=\"2%28%283m-15%29%2B18-15m%2B9%2B4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Next you can remove the parentheses from the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283m-15%29 ALIGN=MIDDLE  ALT=\"%283m-15%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > without changing anything else because there is no minus sign in front of this quantity.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%283m-15%2B18-15m%2B9%2B4%29 ALIGN=MIDDLE  ALT=\"2%283m-15%2B18-15m%2B9%2B4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "For the expression that is still inside of the parentheses, you have 2 terms that contain the variable m, and 4 terms that are just numbers.  Add up all the like terms so that you get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-12m ALIGN=MIDDLE  ALT=\"-12m\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2B16 ALIGN=MIDDLE  ALT=\"%2B16\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  This is where we are applying the Associative and Commutative Properties.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%28-12m%2B16%29 ALIGN=MIDDLE  ALT=\"2%28-12m%2B16%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "One last application of the Distributive Property and we are done:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-24m%2B32 ALIGN=MIDDLE  ALT=\"-24m%2B32\"   DISABLED_style= \"max-width:90%; height:auto;\" >, or it might be more neatly put <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=32-24m ALIGN=MIDDLE  ALT=\"32-24m\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Hope that helps.  I hope you and your family have a joyous holiday season.<BR>\n" );
document.write( "John </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );