document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=968351>Question 968351</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Given a 10 cm by 20 cm piece of paper, if you cut out four equal squares from the corners and fold up the resulting sides you will create an open box. Write an expression for the volume of this box in terms of the side length of each cut&#8208;out square, x. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #591795 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=591795\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the length of the box will be 20 - 2x.<BR>\n" );
document.write( "the width of the box will be 10 - 2x.<BR>\n" );
document.write( "the height of the box will be x.\r<BR>\n" );
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document.write( "the volume of the box is length * width * height.\r<BR>\n" );
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document.write( "this would become v = (20-2x) * (10-2x) * x\r<BR>\n" );
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document.write( "you would then simplify this by performing the indicated operations to get:\r<BR>\n" );
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document.write( "v = (200 - 40x - 20x + 4x^2) * x which would become:\r<BR>\n" );
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document.write( "v = (200 - 60x + 4x^2) * x which would become:\r<BR>\n" );
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document.write( "v = 200x - 60x^2 + 4x^3 which would then be written in standard form as:\r<BR>\n" );
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document.write( "v = 4x^3 - 60x^2 + 200x.\r<BR>\n" );
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document.write( "for example:\r<BR>\n" );
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document.write( "assume the value of x is 2.\r<BR>\n" );
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document.write( "the length of the box after cutting out the corners is equal to 20 - 4 = 16.<BR>\n" );
document.write( "the width of the box after cutting out the corners is equal to 10 - 4 = 6.<BR>\n" );
document.write( "the height of the box is equal to 2.\r<BR>\n" );
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document.write( "the volume is 16 * 6 * 2 = 192.\r<BR>\n" );
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document.write( "per the formjula of y = 4x^3 - 60x^2 + 200x, when you replace x with x, you get y = 4(2)^3 - 60*(2)^2 + 200*(2) which results in y = 4*8 - 60*4 + 200*2 which results in y = 32 - 240 + 400 which results in y = 192.\r<BR>\n" );
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document.write( "the formula check out ok.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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