document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=986866>Question 986866</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Im not sure how to factor and simplify this  (x+3)^(1/2)-(x+3)^(3/2)\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 #607638 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=607638\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z+=+%28x%2B3%29%5E%281%2F2%29%5E%22%22 ALIGN=MIDDLE  ALT=\"z+=+%28x%2B3%29%5E%281%2F2%29%5E%22%22\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "If we cube both sides of the equation above, we get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z%5E3+=+%28%28x%2B3%29%5E%281%2F2%29%5E%22%22%29%5E3+=+%28x%2B3%29%5E%283%2F2%29 ALIGN=MIDDLE  ALT=\"z%5E3+=+%28%28x%2B3%29%5E%281%2F2%29%5E%22%22%29%5E3+=+%28x%2B3%29%5E%283%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "This means the original expression <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B3%29%5E%281%2F2%29%5E%22%22-%28x%2B3%29%5E%283%2F2%29 ALIGN=MIDDLE  ALT=\"%28x%2B3%29%5E%281%2F2%29%5E%22%22-%28x%2B3%29%5E%283%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > is equivalent to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z-z%5E3 ALIGN=MIDDLE  ALT=\"z-z%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "we can factor out a 'z' to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z-z%5E3=z%281-z%5E2%29 ALIGN=MIDDLE  ALT=\"z-z%5E3=z%281-z%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Then use the difference of squares law <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z%281-z%5E2%29=z%281-z%29%281%2Bz%29 ALIGN=MIDDLE  ALT=\"z%281-z%5E2%29=z%281-z%29%281%2Bz%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "-------------------------------------------------------\r<BR>\n" );
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document.write( "So, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z-z%5E3=z%281-z%29%281%2Bz%29 ALIGN=MIDDLE  ALT=\"z-z%5E3=z%281-z%29%281%2Bz%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now replace each 'z' with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B3%29%5E%281%2F2%29%5E%22%22 ALIGN=MIDDLE  ALT=\"%28x%2B3%29%5E%281%2F2%29%5E%22%22\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z-z%5E3=z%281-z%29%281%2Bz%29 ALIGN=MIDDLE  ALT=\"z-z%5E3=z%281-z%29%281%2Bz%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B3%29%5E%281%2F2%29%5E%22%22-%28%28x%2B3%29%5E%281%2F2%29%5E%22%22%29%5E3=%28x%2B3%29%5E%281%2F2%29%5E%22%22%281-%28x%2B3%29%5E%281%2F2%29%5E%22%22%29%281%2B%28x%2B3%29%5E%281%2F2%29%5E%22%22%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B3%29%5E%281%2F2%29%5E%22%22-%28x%2B3%29%5E%283%2F2%29%5E%22%22=%28x%2B3%29%5E%281%2F2%29%5E%22%22%281-%28x%2B3%29%5E%281%2F2%29%5E%22%22%29%281%2B%28x%2B3%29%5E%281%2F2%29%5E%22%22%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Yes it's very ugly, but it's a factored form of the original expression\r<BR>\n" );
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document.write( "The fully factored form is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B3%29%5E%281%2F2%29%5E%22%22%281-%28x%2B3%29%5E%281%2F2%29%5E%22%22%29%281%2B%28x%2B3%29%5E%281%2F2%29%5E%22%22%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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