document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1041509>Question 1041509</A>: <I><SPAN STYLE=\"word-break: break-all;\"> a cubical container for shipping computer components is formed by coating a metal mold with polystyrene. If the metal mold is a cube with sides x centimeters long and the polystyrene coating is 2 centimeters thick, write an algebraic expression in terms of x that represents the volume of the polystyrene used to construct the container. Simplify the expression. (Recall: The volume V of a cube with sides of length t is given by V = t^3.) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #656486 by </B><A HREF=/tutors/aboutme.mpl?userid=Boreal><B>Boreal(15235)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Boreal><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=Boreal><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=656486\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> With a cube and polystyrene 2 cm thick, each side becomes (t+4) cm thick<BR>\n" );
document.write( "The volume is (t+4)^3=t^3+12t^2+48t+64.<BR>\n" );
document.write( "That is through the binomial expansion.<BR>\n" );
document.write( "You can foil out (t+4)^2=t^2+8t+16<BR>\n" );
document.write( "multiply that by (t+4)<BR>\n" );
document.write( "=t^3+4t^2+8*t^2+32t+16t+64, which is the same thing.<BR>\n" );
document.write( "The volume of the metal mold is t^3<BR>\n" );
document.write( "That is subtracted from the expansion, and the volume of the polystyrene is<BR>\n" );
document.write( "12t^2+48t+64 units cm^3<BR>\n" );
document.write( "or<BR>\n" );
document.write( "4(3t^2+12t+16) units are cm^3<BR>\n" );
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document.write( "can check with a cube 6 cm on a side and the polystyrene cover will be a cube 10 cm on a side<BR>\n" );
document.write( "The difference between the cubes is 1000 cm^3-216 cm^3=784 cm^3<BR>\n" );
document.write( "using 4(3*36+12(6)+16)=4(108+72+16)=4(196)=784 cm^3<BR>\n" );
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