document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=711333>Question 711333</A>: <I><SPAN STYLE=\"word-break: break-all;\"> cube root of 2(cube root of 4 subtract 2 times the cube root of 32) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #437512 by </B><A HREF=/tutors/aboutme.mpl?userid=jsmallt9><B>jsmallt9(3758)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jsmallt9><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=437512\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> If<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=root%283%2C+2%29%28root%283%2C+4%29-2%2Aroot%283%2C+32%29%29 ALIGN=MIDDLE  ALT=\"root%283%2C+2%29%28root%283%2C+4%29-2%2Aroot%283%2C+32%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "is the correct expression then please post it as:<BR>\n" );
document.write( "(cube root of 2)((cube root of 4) subtract (2 times the cube root of 32))<BR>\n" );
document.write( "The extra parentheses make it clear. Without them<BR>\n" );
document.write( "cube root of 2(cube root of 4 subtract 2 times the cube root of 32)<BR>\n" );
document.write( "could be interpreted as:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=root%283%2C+2%2Aroot%283%2C+4+-+2%2Aroot%283%2C+32%29%29%29 ALIGN=MIDDLE  ALT=\"root%283%2C+2%2Aroot%283%2C+4+-+2%2Aroot%283%2C+32%29%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "If<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=root%283%2C+2%29%28root%283%2C+4%29-2%2Aroot%283%2C+32%29%29 ALIGN=MIDDLE  ALT=\"root%283%2C+2%29%28root%283%2C+4%29-2%2Aroot%283%2C+32%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "is not correct then you will have to re-post your question because I'm going to simplify this expression.<br><BR>\n" );
document.write( "We could start with either using the Distributive Property to multiply by the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=root%283%2C+2%29 ALIGN=MIDDLE  ALT=\"root%283%2C+2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or we could simplify <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=root%283%2C+32%29 ALIGN=MIDDLE  ALT=\"root%283%2C+32%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > since 8 is a factor of 32 and 8 is a perfect cube (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8+=+2%5E3 ALIGN=MIDDLE  ALT=\"8+=+2%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" >). Looking ahead I can see that using the Distributive Property first will make the rest much easier. So that is how I will start:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=root%283%2C+2%29%2Aroot%283%2C+4%29-root%283%2C+2%29%2A2%2Aroot%283%2C+32%29%29 ALIGN=MIDDLE  ALT=\"root%283%2C+2%29%2Aroot%283%2C+4%29-root%283%2C+2%29%2A2%2Aroot%283%2C+32%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Multiplying the roots together, using the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=root%28a%2C+p%29%2Aroot%28a%2C+q%29+=+root%28a%2C+p%2Aq%29 ALIGN=MIDDLE  ALT=\"root%28a%2C+p%29%2Aroot%28a%2C+q%29+=+root%28a%2C+p%2Aq%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > property of radicals we get:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=root%283%2C+2%2A4%29-2%2Aroot%283%2C+2%2A32%29%29 ALIGN=MIDDLE  ALT=\"root%283%2C+2%2A4%29-2%2Aroot%283%2C+2%2A32%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Simplifying inside the radicals we get:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=root%283%2C+8%29-2%2Aroot%283%2C+64%29%29 ALIGN=MIDDLE  ALT=\"root%283%2C+8%29-2%2Aroot%283%2C+64%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "8, as was mentioned earlier, is a perfect cube. And so is 64! <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=64+=+4%5E3 ALIGN=MIDDLE  ALT=\"64+=+4%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" >. So both cube roots simplify:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2-2%2A4 ALIGN=MIDDLE  ALT=\"2-2%2A4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Continuing to simplify:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2-8 ALIGN=MIDDLE  ALT=\"2-8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-6 ALIGN=MIDDLE  ALT=\"-6\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );