document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=80446>Question 80446</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Let us use the following problem statement, to discuss differences between a term and a factor?  \r<BR>\n" );
document.write( "\n" );
document.write( "Let us consider the price of a cube shaped stone of length R inches.  The cost of an unpolished stone is proportional to its weight which is proportional to cube of its length, i.e. R*R*R or R^3  cubic inches.  <BR>\n" );
document.write( " <BR>\n" );
document.write( "Assuming that it cost $1000 for one cubic inch of raw stone, we can write the cost of one raw stone as 1000R^3.  e.g. if R is 2 inches, the cost of raw stone is 1000 * 2^3 or  $8000.<BR>\n" );
document.write( " <BR>\n" );
document.write( " Let cost of polishing a square inch of the surface area of the rock is $100.  Noting that the surface area of rock is proportional to the square of length, i.e.  R^2  we have the cost of polishing the stone as 600R^2 (note there are 6 faces to a cube). In the above example where R is 2 inches, the cost of polishing is 600 * 2^2 or $2400.<BR>\n" );
document.write( " <BR>\n" );
document.write( "Assuming there is no other cost, the cost of a finished stone would require summing up the cost of raw stone (by weight)  and cost of polishing.  <BR>\n" );
document.write( "Write down an  expression  for the cost of the finished stone of length R and identify the different terms in it. \r<BR>\n" );
document.write( "\n" );
document.write( "Can you factor these terms?  Is there any factor common to different terms here? \r<BR>\n" );
document.write( "\n" );
document.write( "What is the expression for cost of 5 finished stones of length X?<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #805003 by </B><A HREF=/tutors/aboutme.mpl?userid=CubeyThePenguin><B>CubeyThePenguin(3113)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=CubeyThePenguin><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=CubeyThePenguin><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=805003\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> cost of 1 raw stone = 1000x^3<BR>\n" );
document.write( "cost to polish stone = 600x^2\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "5 stones: 5000x^3 + 3000x^2 </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );