document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=152956>Question 152956</A>: <I><SPAN STYLE=\"word-break: break-all;\"> How do I factor completely x^8-1? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #112417 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=112417\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E8-1 ALIGN=MIDDLE  ALT=\"x%5E8-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given expression\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5E4%29%5E2-%281%29%5E2 ALIGN=MIDDLE  ALT=\"%28x%5E4%29%5E2-%281%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Rewrite <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E8 ALIGN=MIDDLE  ALT=\"x%5E8\"   DISABLED_style= \"max-width:90%; height:auto;\" > as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5E4%29%5E2 ALIGN=MIDDLE  ALT=\"%28x%5E4%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Rewrite <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1 ALIGN=MIDDLE  ALT=\"1\"   DISABLED_style= \"max-width:90%; height:auto;\" > as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%29%5E2 ALIGN=MIDDLE  ALT=\"%281%29%5E2\"   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%5E4%2B1%29%28x%5E4-1%29 ALIGN=MIDDLE  ALT=\"%28x%5E4%2B1%29%28x%5E4-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Factor using the difference of squares formula. Remember, the difference of squares formula is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%5E2-B%5E2=%28A%2BB%29%28A-B%29 ALIGN=MIDDLE  ALT=\"A%5E2-B%5E2=%28A%2BB%29%28A-B%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%5E4%2B1%29%28%28x%5E2%29%5E2-%281%29%5E2%29 ALIGN=MIDDLE  ALT=\"%28x%5E4%2B1%29%28%28x%5E2%29%5E2-%281%29%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Rewrite <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E4 ALIGN=MIDDLE  ALT=\"x%5E4\"   DISABLED_style= \"max-width:90%; height:auto;\" > as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5E2%29%5E2 ALIGN=MIDDLE  ALT=\"%28x%5E2%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Rewrite <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1 ALIGN=MIDDLE  ALT=\"1\"   DISABLED_style= \"max-width:90%; height:auto;\" > as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%29%5E2 ALIGN=MIDDLE  ALT=\"%281%29%5E2\"   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%5E4%2B1%29%28x%5E2%2B1%29%28x%5E2-1%29 ALIGN=MIDDLE  ALT=\"%28x%5E4%2B1%29%28x%5E2%2B1%29%28x%5E2-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Factor <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5E2%29%5E2-%281%29%5E2 ALIGN=MIDDLE  ALT=\"%28x%5E2%29%5E2-%281%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > using the difference of squares formula\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5E4%2B1%29%28x%5E2%2B1%29%28x%5E2-%281%29%5E2%29 ALIGN=MIDDLE  ALT=\"%28x%5E4%2B1%29%28x%5E2%2B1%29%28x%5E2-%281%29%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >  Rewrite <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1 ALIGN=MIDDLE  ALT=\"1\"   DISABLED_style= \"max-width:90%; height:auto;\" > as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%29%5E2 ALIGN=MIDDLE  ALT=\"%281%29%5E2\"   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%5E4%2B1%29%28x%5E2%2B1%29%28x%2B1%29%28x-1%29 ALIGN=MIDDLE  ALT=\"%28x%5E4%2B1%29%28x%5E2%2B1%29%28x%2B1%29%28x-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >   Factor <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-%281%29%5E2 ALIGN=MIDDLE  ALT=\"x%5E2-%281%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > using the difference of squares formula \r<BR>\n" );
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document.write( "So the expression <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E8-1 ALIGN=MIDDLE  ALT=\"x%5E8-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > factors to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5E4%2B1%29%28x%5E2%2B1%29%28x%2B1%29%28x-1%29 ALIGN=MIDDLE  ALT=\"%28x%5E4%2B1%29%28x%5E2%2B1%29%28x%2B1%29%28x-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "In other words, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E8-1=%28x%5E4%2B1%29%28x%5E2%2B1%29%28x%2B1%29%28x-1%29 ALIGN=MIDDLE  ALT=\"x%5E8-1=%28x%5E4%2B1%29%28x%5E2%2B1%29%28x%2B1%29%28x-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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