document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=172778>Question 172778</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The first three terms in the expansion of (1+ay)^n are 1,12y, and 68y^2\r<BR>\n" );
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document.write( "Evaluate a and n.  Use the fact that:\r<BR>\n" );
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document.write( "(1+ay)^n=1+nay+n(n-1)/2(ay)^2+...\r<BR>\n" );
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document.write( "my teacher told me to use: c(n,k)(1)^n(ay)^k to figure it out and to refer to pascals triangle, But it hasnt helped.  I would very much appricate if someone could help.<BR>\n" );
document.write( "Thanks </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #127654 by </B><A HREF=/tutors/aboutme.mpl?userid=vleith><B>vleith(2983)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=vleith><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=127654\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> First three terms are 1, 12y and 68y^2<BR>\n" );
document.write( "Your hint says (1+ay)^n=1+nay+n(n-1)/2(ay)^2+<BR>\n" );
document.write( "so (1+ay)^n=1+12y+68y^2+...<BR>\n" );
document.write( "12y=nay, so na=12 and a=12/n<BR>\n" );
document.write( "68y^2 = (n(n-1)/2)(ay)^2 = (n(n-1)/2)a^2y^2. so (n(n-1)/2)a^2 = 68\r<BR>\n" );
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document.write( "Now substitute the value for a into the second equation and solve<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n%28n-1%29a%5E2%2F2+=+68 ALIGN=MIDDLE  ALT=\"n%28n-1%29a%5E2%2F2+=+68\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28n%5E2-n%29%2F2%29+%2A+%2812%2Fn%29%5E2+=+68 ALIGN=MIDDLE  ALT=\"%28%28n%5E2-n%29%2F2%29+%2A+%2812%2Fn%29%5E2+=+68\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28n%5E2-n%29%28144%2F2%29+%2F+%28n%5E2%29+=+68+ ALIGN=MIDDLE  ALT=\"%28n%5E2-n%29%28144%2F2%29+%2F+%28n%5E2%29+=+68+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28n%5E2+-n%2972+=+68n%5E2 ALIGN=MIDDLE  ALT=\"%28n%5E2+-n%2972+=+68n%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=72n%5E2+-+72n+=+68n%5E2 ALIGN=MIDDLE  ALT=\"72n%5E2+-+72n+=+68n%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4n%5E2+=+72n ALIGN=MIDDLE  ALT=\"4n%5E2+=+72n\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4n+=+72 ALIGN=MIDDLE  ALT=\"4n+=+72\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n+=+18 ALIGN=MIDDLE  ALT=\"n+=+18\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "so a = 2/3\r<BR>\n" );
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document.write( "now check against the hint to see if the values work<BR>\n" );
document.write( "a*n = (2/3)*18 = 12. so far so good<BR>\n" );
document.write( "(18*17/2)*(4/9) = 68\r<BR>\n" );
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document.write( " </SPAN>\n" );
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