document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=111367>Question 111367</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Prove a^3-64/a^2-16=a^2+4a+16/a+4 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #81187 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=81187\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> For this problem we need to use the difference of squares and the difference of cubes formulas. \r<BR>\n" );
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document.write( "Remember the difference of squares formula is:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-y%5E2=%28x%2By%29%28x-y%29 ALIGN=MIDDLE  ALT=\"x%5E2-y%5E2=%28x%2By%29%28x-y%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "and the difference of cubes formula is:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E3-y%5E3=%28x-y%29%28x%5E2%2Bxy%2By%5E2%29 ALIGN=MIDDLE  ALT=\"x%5E3-y%5E3=%28x-y%29%28x%5E2%2Bxy%2By%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So rewrite the numerator <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E3-64 ALIGN=MIDDLE  ALT=\"a%5E3-64\"   DISABLED_style= \"max-width:90%; height:auto;\" > as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28a%29%5E3-%284%29%5E3 ALIGN=MIDDLE  ALT=\"%28a%29%5E3-%284%29%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" > notice how <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=a ALIGN=MIDDLE  ALT=\"x=a\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=b ALIGN=MIDDLE  ALT=\"y=b\"   DISABLED_style= \"max-width:90%; height:auto;\" > for the formula <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-y%5E2=%28x%2By%29%28x-y%29 ALIGN=MIDDLE  ALT=\"x%5E2-y%5E2=%28x%2By%29%28x-y%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Now factor <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28a%29%5E3-%284%29%5E3 ALIGN=MIDDLE  ALT=\"%28a%29%5E3-%284%29%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" > to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28a-4%29%28a%5E2%2B4a%2B16%29 ALIGN=MIDDLE  ALT=\"%28a-4%29%28a%5E2%2B4a%2B16%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So our expression now looks like this: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28a-4%29%28a%5E2%2B4a%2B16%29%2F%28a%5E2-16%29 ALIGN=MIDDLE  ALT=\"%28a-4%29%28a%5E2%2B4a%2B16%29%2F%28a%5E2-16%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now factor the denominator using the difference of squares\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28a-4%29%28a%5E2%2B4a%2B16%29%2F%28%28a%2B4%29%28a-4%29%29 ALIGN=MIDDLE  ALT=\"%28a-4%29%28a%5E2%2B4a%2B16%29%2F%28%28a%2B4%29%28a-4%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Cancel like terms\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cross%28%28a-4%29%29%28a%5E2%2B4a%2B16%29%2F%28%28a%2B4%29cross%28%28a-4%29%29%29 ALIGN=MIDDLE  ALT=\"cross%28%28a-4%29%29%28a%5E2%2B4a%2B16%29%2F%28%28a%2B4%29cross%28%28a-4%29%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Simplify\r<BR>\n" );
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document.write( "So this shows that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28a%5E3-64%29%2F%28a%5E2-16%29 ALIGN=MIDDLE  ALT=\"%28a%5E3-64%29%2F%28a%5E2-16%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > simplifies to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28a%5E2%2B4a%2B16%29%2F%28a%2B4%29 ALIGN=MIDDLE  ALT=\"%28a%5E2%2B4a%2B16%29%2F%28a%2B4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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