document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=10762>Question 10762</A>: <I><SPAN STYLE=\"word-break: break-all;\"> My question is:<BR>\n" );
document.write( "The length, width, and height of a rectanglar box are consecutive integers,and the largest dimension is k cm. Find the volume V of the box. (hint: V=lwh)\r<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 #5650 by </B><A HREF=/tutors/aboutme.mpl?userid=prince_abubu><B>prince_abubu(198)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=prince_abubu><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=5650\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> OK. The dimensions, length, width, and height, are consecutive integers. This means they're \"together\" without skipping integers, and they're different from each other, like (5,6,7) or (101,102,103). IF the largest of the dimensions is k, then the other two HAVE TO BE (k-1) and (k-2). Suppose that k is any integer. (k-1) and (k-2) will be forced to be the next two integers less than k. (They're \"together\").\r<BR>\n" );
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document.write( "So the volume is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+V+=+k%28k-1%29%28k-2%29+ ALIGN=MIDDLE  ALT=\"+V+=+k%28k-1%29%28k-2%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > <------ We can leave it at this point, but I think they may want us to expand.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+V+=+%28k%5E2+-+k%29%28k+-+2%29+ ALIGN=MIDDLE  ALT=\"+V+=+%28k%5E2+-+k%29%28k+-+2%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > <----- we just multiplied the k and the k-1 by distributive property.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+V+=+k%5E3+-+3k+%2B+2k+ ALIGN=MIDDLE  ALT=\"+V+=+k%5E3+-+3k+%2B+2k+\"   DISABLED_style= \"max-width:90%; height:auto;\" > <-------- performed FOIL. This is as far as we can get. </SPAN>\n" );
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