document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=673284>Question 673284</A>: <I><SPAN STYLE=\"word-break: break-all;\"> How do I simplify the expression and justify each step? By justify I mean each time you simplify would that step be distributive, associative, commutative etc.<BR>\n" );
document.write( "29c + (-29c) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #418631 by </B><A HREF=/tutors/aboutme.mpl?userid=KMST><B>KMST(5328)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=KMST><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=KMST><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=418631\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> WARNING:<BR>\n" );
document.write( "Different books/teachers may give slightly different names to the same properties.<BR>\n" );
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document.write( "IF YOU MUST CHOOSE JUST ONE PROPERTY, AS IN A MULTIPLE CHOICE QUESTION,<BR>\n" );
document.write( "then it would be simple.<BR>\n" );
document.write( "I could say that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-29c ALIGN=MIDDLE  ALT=\"-29c\"   DISABLED_style= \"max-width:90%; height:auto;\" > obviously means the additive inverse of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=29c ALIGN=MIDDLE  ALT=\"29c\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "Then I would say that<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=29c+%2B+%28-29c%29=0 ALIGN=MIDDLE  ALT=\"29c+%2B+%28-29c%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the Additive Identity Property.<BR>\n" );
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document.write( "IF A FULL EXPLANATION IS EXPECTED,<BR>\n" );
document.write( "it may be more complicated.<BR>\n" );
document.write( "Unfortunately, I suspect they want to make it more complicated, and we would need to invoke 3 or more properties.<BR>\n" );
document.write( "If it is interpreted as just <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-29c=-29%2Ac ALIGN=MIDDLE  ALT=\"-29c=-29%2Ac\"   DISABLED_style= \"max-width:90%; height:auto;\" >, we could say that<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=29c+%2B+%28-29c%29=%2829%2B%28-29%29%29%2Ac ALIGN=MIDDLE  ALT=\"29c+%2B+%28-29c%29=%2829%2B%28-29%29%29%2Ac\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the application of the Distributive Property.<BR>\n" );
document.write( "Then,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2829%2B%28-29%29%29%2Ac=0%2Ac ALIGN=MIDDLE  ALT=\"%2829%2B%28-29%29%29%2Ac=0%2Ac\"   DISABLED_style= \"max-width:90%; height:auto;\" > Additive Identity Property,<BR>\n" );
document.write( "and finally,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0%2Ac=0 ALIGN=MIDDLE  ALT=\"0%2Ac=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Zero Property<BR>\n" );
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document.write( "IF THEY WANT TO MAKE YOU EXPLAIN EVEN MORE:<BR>\n" );
document.write( "The Distributive Property is usually represented in the form<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c%28a%2Bb%29=c%2Aa%2Bc%2Ab ALIGN=MIDDLE  ALT=\"c%28a%2Bb%29=c%2Aa%2Bc%2Ab\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "In this case we have <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%2Ac%2Bb%2Ac=%28a%2Bb%29c ALIGN=MIDDLE  ALT=\"a%2Ac%2Bb%2Ac=%28a%2Bb%29c\"   DISABLED_style= \"max-width:90%; height:auto;\" >, with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=29 ALIGN=MIDDLE  ALT=\"a=29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=-29 ALIGN=MIDDLE  ALT=\"b=-29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "That is usually referred to as \"taking out a common factor\".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%2Ac%2Bb%2Ac=%28a%2Bb%29c ALIGN=MIDDLE  ALT=\"a%2Ac%2Bb%2Ac=%28a%2Bb%29c\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the same (read backwards) as<BR>\n" );
document.write( "the usual <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28a%2Bb%29c=a%2Ac%2Bb%2Ac ALIGN=MIDDLE  ALT=\"%28a%2Bb%29c=a%2Ac%2Bb%2Ac\"   DISABLED_style= \"max-width:90%; height:auto;\" > distributive property.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c%28a%2Bb%29=c%2Aa%2Bc%2Ab ALIGN=MIDDLE  ALT=\"c%28a%2Bb%29=c%2Aa%2Bc%2Ab\"   DISABLED_style= \"max-width:90%; height:auto;\" > and  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28a%2Bb%29c=a%2Ac%2Bb%2Ac ALIGN=MIDDLE  ALT=\"%28a%2Bb%29c=a%2Ac%2Bb%2Ac\"   DISABLED_style= \"max-width:90%; height:auto;\" > are the same thing,<BR>\n" );
document.write( "because of the Commutative Properties for Addition and Multiplication.<BR>\n" );
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