document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=211668>Question 211668</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A cubic shipping container had a volume of v^3 cubic meters. The height of the container was decreased by a whole number of meters and the width was increased by a whole number of meters so that the volume of the container is now v^3+2v^2-3v. Find out the following:\r<BR>\n" );
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document.write( "a.	By how many meters the height was decreased?\r<BR>\n" );
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document.write( "b.	By how many meters the width was increased<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #160004 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=160004\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> If it was a cubic shipping container, then it was a perfect cube making the dimensions of each side = v.<BR>\n" );
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document.write( "original volume = v*v*v = v^3<BR>\n" );
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document.write( "The height was decreased by an integer called a.<BR>\n" );
document.write( "The width was increased by an integer called b.<BR>\n" );
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document.write( "new volume = <BR>\n" );
document.write( "(v-a)*(v-b)*v = v^3 + 2v^2 - 3v<BR>\n" );
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document.write( "If we divide both sides of this equation by v, we get:<BR>\n" );
document.write( "(v-a)*(v+b) = v^2 + 2v - 3<BR>\n" );
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document.write( "if we factor the equation on the right side, we get:<BR>\n" );
document.write( "(v-a)*(v+b) = (v-1)*(v+3)<BR>\n" );
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document.write( "This means that a = 1 and b = 3 will satisfy the equation.<BR>\n" );
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document.write( "The height is reduced by 1 and the width is increased by 2.<BR>\n" );
document.write( "v*v*v = v^3<BR>\n" );
document.write( "(v-1)*(v+3)*v = v^3 + 2v^2 - 3v<BR>\n" );
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document.write( "Answer is:<BR>\n" );
document.write( "height is reduced by 1 and width is increased by 3 meters.<BR>\n" );
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