document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=174067>Question 174067</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A student says he noticed that 39 * 41 = 40 * 40 – 1, and 59 * 61 = 60 * 60 – 1.  He wants to know if this pattern continues.  How do you respond? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #128987 by </B><A HREF=/tutors/aboutme.mpl?userid=loni><B>loni(3)</B></A><img src=\"/images/stars/iconNewId_16x16.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=loni><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=128987\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> OK, that is so:\r<BR>\n" );
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document.write( "(a-b)*(a+b)=a^2+ab-ab-b^2 ; ab-ab=0 , so (a-b)*(a+b)=a^2-b^2. \r<BR>\n" );
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document.write( "In this case b is always b=1 so:\r<BR>\n" );
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document.write( "(a-1)*(a+1)=a^2-1^2; 1^2=1, (a-1)*(a+b)=a^2-1.\r<BR>\n" );
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document.write( "Now when a=40, b=1, <BR>\n" );
document.write( "(40-1)*(40+1)=40^2-1^2;<BR>\n" );
document.write( "(60-1)*(60+1)=60^2-1^2  etc.....\r<BR>\n" );
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document.write( "I hope you like the answer and I am sorry for my bad English. </SPAN>\n" );
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