document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=40998>Question 40998</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Decreasing cube. Each of the three dimensions of a cube with a volume of y to the third power cubic centimeters is decreased by a whole number of centimeters. If the new volume is y-cubed - 13 y-squared + 54y - 72 cubic centimeters and the new width is y - 6 centimeters, then what are the new length and height? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #27108 by </B><A HREF=/tutors/aboutme.mpl?userid=psbhowmick><B>psbhowmick(878)</B></A><img src=\"/images/stars/stars-11.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=psbhowmick><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=psbhowmick><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=27108\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> New volume = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5E3-13y%5E2%2B54y-72 ALIGN=MIDDLE  ALT=\"y%5E3-13y%5E2%2B54y-72\"   DISABLED_style= \"max-width:90%; height:auto;\" > cc.<BR>\n" );
document.write( "Since (y - 6) cm is the new width, so it must be a factor of the new volume.<BR>\n" );
document.write( "So, we will write <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5E3-13y%5E2%2B54y-72 ALIGN=MIDDLE  ALT=\"y%5E3-13y%5E2%2B54y-72\"   DISABLED_style= \"max-width:90%; height:auto;\" > in such a way that (y - 6) may be taken common.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5E3-13y%5E2%2B54y-72 ALIGN=MIDDLE  ALT=\"y%5E3-13y%5E2%2B54y-72\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "= <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5E3-6y%5E2-7y%5E2%2B42y%2B12y-72 ALIGN=MIDDLE  ALT=\"y%5E3-6y%5E2-7y%5E2%2B42y%2B12y-72\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "= <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5E2%28y-6%29-7y%28y-6%29%2B12%28y-6%29 ALIGN=MIDDLE  ALT=\"y%5E2%28y-6%29-7y%28y-6%29%2B12%28y-6%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "= <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28y-6%29%28y%5E2-7y%2B12%29 ALIGN=MIDDLE  ALT=\"%28y-6%29%28y%5E2-7y%2B12%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "= <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28y-6%29%28y%5E2-3y-4y%2B12%29 ALIGN=MIDDLE  ALT=\"%28y-6%29%28y%5E2-3y-4y%2B12%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "= <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28y-6%29%28y%28y-3%29-4%28y-3%29%29 ALIGN=MIDDLE  ALT=\"%28y-6%29%28y%28y-3%29-4%28y-3%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "= <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28y-6%29%28y-3%29%28y-4%29 ALIGN=MIDDLE  ALT=\"%28y-6%29%28y-3%29%28y-4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So clearly (y-3) cm and (y-4) cm are the new length and height respectively.\r<BR>\n" );
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document.write( "[N.B.: (y-3) > (y-4); so (y-3) is length being the longest side] </SPAN>\n" );
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