document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=682117>Question 682117</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 7^12 - 4^12 is exactly divisible by<BR>\n" );
document.write( "A.33<BR>\n" );
document.write( "B.34<BR>\n" );
document.write( "C.35<BR>\n" );
document.write( "D.36\r<BR>\n" );
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document.write( "Explain how? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #423047 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=423047\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <BR>\n" );
document.write( "7^12 - 4^12 \r<BR>\n" );
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document.write( "(7^6)^2 - (4^6)^2 \r<BR>\n" );
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document.write( "(7^6 - 4^6)(7^6 + 4^6) ... Use the difference of squares rule\r<BR>\n" );
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document.write( "((7^3)^2 - (4^3)^2)(7^6 + 4^6)\r<BR>\n" );
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document.write( "(7^3 - 4^3)(7^3 + 4^3)(7^6 + 4^6) ... Use the difference of squares rule\r<BR>\n" );
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document.write( "(7 - 4)(7^2 + 7*4 + 4^2)(7^3 + 4^3)(7^6 + 4^6) ... Use the difference of cubes rule\r<BR>\n" );
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document.write( "(7 - 4)(49 + 28 + 16)(7^3 + 4^3)(7^6 + 4^6)\r<BR>\n" );
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document.write( "(3)(93)(7^3 + 4^3)(7^6 + 4^6)\r<BR>\n" );
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document.write( "(3)(93)(7 + 4)(7^2 - 7*4 + 4^2)(7^6 + 4^6) ... Use the sum of cubes rule\r<BR>\n" );
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document.write( "(3)(93)(7 + 4)(49 - 28 + 16)(7^6 + 4^6)\r<BR>\n" );
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document.write( "(3)(93)(11)(37)(7^6 + 4^6)\r<BR>\n" );
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document.write( "(3*11)(93)(37)(7^6 + 4^6)\r<BR>\n" );
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document.write( "(33)(93)(37)(7^6 + 4^6)\r<BR>\n" );
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document.write( "We can see that 33 is a factor of (33)(93)(37)(7^6 + 4^6), so 33 is also a factor of 7^12 - 4^12 since each line in the work shown above is equivalent to any other line (ie they represent the same number)\r<BR>\n" );
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document.write( "This means that 7^12 - 4^12 is exactly divisible by 33.\r<BR>\n" );
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document.write( "Therefore, the answer is A) 33.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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