document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=255962>Question 255962</A>: <I><SPAN STYLE=\"word-break: break-all;\"> An open box is made from an 8-by-10-inch rectangular piece of cardboard by cutting squares from each corner and folding up the sides. If x represents the side length of the squares, which of the following is a function giving the volume V(x) of the box in terms of x? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #188138 by </B><A HREF=/tutors/aboutme.mpl?userid=NRobinson><B>NRobinson(4)</B></A><img src=\"/images/stars/iconNewId_16x16.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=NRobinson><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=188138\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> To make an open box we can cut squares out of the corners and fold the sides up.  If x is the length of the side we are cutting then when we fold that side up, x will be the height (take a minute to think about what this looks like when you cut out the box length x and then fold that flap up. the x inch piece you cut is the amount you are folding up so that is the height.)\r<BR>\n" );
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document.write( "So x is the height.  We are looking for the volume so we will also need the length and width since the formula for volume is the product (*) of length, width and height.\r<BR>\n" );
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document.write( "We cut off x inches off the length and width on each side (again think about what this looks like). We are taking 2x off each measurement (one x from each end).  So now instead of a length of 8 inches, our length is 8-2x inches.<BR>\n" );
document.write( "Similarly, our width of 10 inches was cut down by 2x also to give us 10-2x inches.\r<BR>\n" );
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document.write( "Now we have in terms of x the length, width and height.  The volume is the product of these three, so substitute them in.  Let V(x) be the volume.\r<BR>\n" );
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document.write( "V(x)=length* width *height= (8-2x)*(10-2x)*(x)\r<BR>\n" );
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document.write( "We'll simplify for fun- FOIL the first two<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=V%28x%29=%2880-20x-16x%2B4x%5E2%29%28x%29 ALIGN=MIDDLE  ALT=\"V%28x%29=%2880-20x-16x%2B4x%5E2%29%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=V%28x%29=%2880-36x%2B4x%5E2%29%28x%29 ALIGN=MIDDLE  ALT=\"V%28x%29=%2880-36x%2B4x%5E2%29%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Distribute x over each term<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=V%28x%29=80x-36x%5E2%2B4x%5E3 ALIGN=MIDDLE  ALT=\"V%28x%29=80x-36x%5E2%2B4x%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Note that the volume is going to be in cubic inches (inch*inch*inch)=(inch^3)<BR>\n" );
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