document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=146745>Question 146745</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Write an algebraic expression that proves the difference of the square of any two odd numbers must be divisible by 8. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #107170 by </B><A HREF=/tutors/aboutme.mpl?userid=Alan3354><B>Alan3354(69443)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Alan3354><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=Alan3354><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=107170\">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=%28n%2B2%29%5E2+-+n%5E2+=+n%5E2+%2B+4n+%2B4+-n%5E2 ALIGN=MIDDLE  ALT=\"%28n%2B2%29%5E2+-+n%5E2+=+n%5E2+%2B+4n+%2B4+-n%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "= 4n + 4<BR>\n" );
document.write( "=4(n + 1)<BR>\n" );
document.write( "Since n is odd, n+1 is even, meaning it has at least one factor of 2.<BR>\n" );
document.write( "4 times that has to be divisible by 8, as it adds 2 more factors of 2. </SPAN>\n" );
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