document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1054348>Question 1054348</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Simplify.\r<BR>\n" );
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document.write( "(x^16-y^16)/(x^8-y^8) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #669565 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=669565\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> x^16 - y^16 = (x^8)^2 - (y^8)^2\r<BR>\n" );
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document.write( "your equation becomes:\r<BR>\n" );
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document.write( "((x^8)^2 - (y^8)^2) / (x^8 - y^8)\r<BR>\n" );
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document.write( "since a^2 - b^2 = (a - b) * (a + b), we can make a = x^8 and b = y^8 and your expression will become:\r<BR>\n" );
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document.write( "((x^8 - y^8) * (x^8 + y^8)) / (x^8 - y^8)\r<BR>\n" );
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document.write( "the (x^8 - y^8) in the numerator and denominator cancel out and you are left with:\r<BR>\n" );
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document.write( "(x^8 + y^8).\r<BR>\n" );
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document.write( "that's your answer.\r<BR>\n" );
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document.write( "you can confirm the solution is correct by assuming a random value for x and a different random value for y and evaluating the original equation and then the final solution to see that they yield the same answer.\r<BR>\n" );
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document.write( "i used x = 5 and y = 3 and i got 397186 for both expressions.\r<BR>\n" );
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document.write( "i evaluated:\r<BR>\n" );
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document.write( "(x^16 - y^16) / (x^8 - y^8)\r<BR>\n" );
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document.write( "and i evaluated:\r<BR>\n" );
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document.write( "(x^8 + y^8)\r<BR>\n" );
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document.write( " </SPAN>\n" );
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