document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=166270>Question 166270</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0395977258/algebrahomeworkh>Algebra and Trigonometry Structure and Method book 2</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> I have been working on this math problem and I can't figure it out. I was wondering if someone could help me? Please and Thank You!!! I would deeply appreciate it!!\r<BR>\n" );
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document.write( "Factoring Quadratic Polynomials<BR>\n" );
document.write( "Factor completely. If the polynomial is prime, say so.<BR>\n" );
document.write( "x^6-64y^6 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #122536 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=122536\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E6-64y%5E6 ALIGN=MIDDLE  ALT=\"x%5E6-64y%5E6\"   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%5E3%29%5E2-64y%5E6 ALIGN=MIDDLE  ALT=\"%28x%5E3%29%5E2-64y%5E6\"   DISABLED_style= \"max-width:90%; height:auto;\" > Rewrite <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E6 ALIGN=MIDDLE  ALT=\"x%5E6\"   DISABLED_style= \"max-width:90%; height:auto;\" > as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5E3%29%5E2 ALIGN=MIDDLE  ALT=\"%28x%5E3%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%5E3%29%5E2-%288y%5E3%29%5E2 ALIGN=MIDDLE  ALT=\"%28x%5E3%29%5E2-%288y%5E3%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Rewrite <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=64y%5E6 ALIGN=MIDDLE  ALT=\"64y%5E6\"   DISABLED_style= \"max-width:90%; height:auto;\" > as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%288y%5E3%29%5E2 ALIGN=MIDDLE  ALT=\"%288y%5E3%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "Notice how we have a difference of squares. So let's use the difference of squares formula <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;\" > to factor the expression:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5E3%2B8y%5E3%29%28x%5E3-8y%5E3%29 ALIGN=MIDDLE  ALT=\"%28x%5E3%2B8y%5E3%29%28x%5E3-8y%5E3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Factor the expression using the difference of squares.\r<BR>\n" );
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document.write( "Now let's factor <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E3%2B8y%5E3 ALIGN=MIDDLE  ALT=\"x%5E3%2B8y%5E3\"   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=x%5E3%2B8y%5E3 ALIGN=MIDDLE  ALT=\"x%5E3%2B8y%5E3\"   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%29%5E3%2B%282y%29%5E3 ALIGN=MIDDLE  ALT=\"%28x%29%5E3%2B%282y%29%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" > Rewrite <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E3 ALIGN=MIDDLE  ALT=\"x%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" > as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%29%5E3 ALIGN=MIDDLE  ALT=\"%28x%29%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Rewrite <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8y%5E3 ALIGN=MIDDLE  ALT=\"8y%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" > as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282y%29%5E3 ALIGN=MIDDLE  ALT=\"%282y%29%5E3\"   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%2B2y%29%28%28x%29%5E2-%28x%29%282y%29%2B%282y%29%5E2%29 ALIGN=MIDDLE  ALT=\"%28x%2B2y%29%28%28x%29%5E2-%28x%29%282y%29%2B%282y%29%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Now factor by using the sum of cubes formula. Remember the <a  rel=nofollow HREF=\"http://www.purplemath.com/modules/specfact2.htm\">sum of cubes formula</a> is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%5E3%2BB%5E3=%28A%2BB%29%28A%5E2-AB%2BB%5E2%29 ALIGN=MIDDLE  ALT=\"A%5E3%2BB%5E3=%28A%2BB%29%28A%5E2-AB%2BB%5E2%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%2B2y%29%28x%5E2-2xy%2B4y%5E2%29 ALIGN=MIDDLE  ALT=\"%28x%2B2y%29%28x%5E2-2xy%2B4y%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply\r<BR>\n" );
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document.write( "So <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E3%2B8y%5E3 ALIGN=MIDDLE  ALT=\"x%5E3%2B8y%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" > factors to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B2y%29%28x%5E2-2xy%2B4y%5E2%29 ALIGN=MIDDLE  ALT=\"%28x%2B2y%29%28x%5E2-2xy%2B4y%5E2%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%5E3%2B8y%5E3=%28x%2B2y%29%28x%5E2-2xy%2B4y%5E2%29 ALIGN=MIDDLE  ALT=\"x%5E3%2B8y%5E3=%28x%2B2y%29%28x%5E2-2xy%2B4y%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now let's factor <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E3-8y%5E3 ALIGN=MIDDLE  ALT=\"x%5E3-8y%5E3\"   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=x%5E3-8y%5E3 ALIGN=MIDDLE  ALT=\"x%5E3-8y%5E3\"   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%29%5E3-%282y%29%5E3 ALIGN=MIDDLE  ALT=\"%28x%29%5E3-%282y%29%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" > Rewrite <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E3 ALIGN=MIDDLE  ALT=\"x%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" > as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%29%5E3 ALIGN=MIDDLE  ALT=\"%28x%29%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Rewrite <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8y%5E3 ALIGN=MIDDLE  ALT=\"8y%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" > as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282y%29%5E3 ALIGN=MIDDLE  ALT=\"%282y%29%5E3\"   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-2y%29%28%28x%29%5E2%2B%28x%29%282y%29%2B%282y%29%5E2%29 ALIGN=MIDDLE  ALT=\"%28x-2y%29%28%28x%29%5E2%2B%28x%29%282y%29%2B%282y%29%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Now factor by using the difference of cubes formula. Remember the <a  rel=nofollow HREF=\"http://www.purplemath.com/modules/specfact2.htm\">difference of cubes formula</a> is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%5E3-B%5E3=%28A-B%29%28A%5E2%2BAB%2BB%5E2%29 ALIGN=MIDDLE  ALT=\"A%5E3-B%5E3=%28A-B%29%28A%5E2%2BAB%2BB%5E2%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-2y%29%28x%5E2%2B2xy%2B4y%5E2%29 ALIGN=MIDDLE  ALT=\"%28x-2y%29%28x%5E2%2B2xy%2B4y%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply\r<BR>\n" );
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document.write( "So <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E3-8y%5E3 ALIGN=MIDDLE  ALT=\"x%5E3-8y%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" > factors to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-2y%29%28x%5E2%2B2xy%2B4y%5E2%29 ALIGN=MIDDLE  ALT=\"%28x-2y%29%28x%5E2%2B2xy%2B4y%5E2%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%5E3-8y%5E3=%28x-2y%29%28x%5E2%2B2xy%2B4y%5E2%29 ALIGN=MIDDLE  ALT=\"x%5E3-8y%5E3=%28x-2y%29%28x%5E2%2B2xy%2B4y%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Answer:\r<BR>\n" );
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document.write( "So <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E6-64y%5E6 ALIGN=MIDDLE  ALT=\"x%5E6-64y%5E6\"   DISABLED_style= \"max-width:90%; height:auto;\" > completely factors to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B2y%29%28x-2y%29%28x%5E2-2xy%2B4y%5E2%29%28x%5E2%2B2xy%2B4y%5E2%29 ALIGN=MIDDLE  ALT=\"%28x%2B2y%29%28x-2y%29%28x%5E2-2xy%2B4y%5E2%29%28x%5E2%2B2xy%2B4y%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > (I just rearranged the factors a bit)\r<BR>\n" );
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document.write( "Note: the order of the factors does not matter  </SPAN>\n" );
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