document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1198624>Question 1198624</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the 7th term of the binomial (x+y)^9.\r<BR>\n" );
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document.write( "One of the following is the correct answer. Which one?\r<BR>\n" );
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document.write( "A) 84x^3 y^6<BR>\n" );
document.write( "B) 36x^2 y^7<BR>\n" );
document.write( "C) 210x^3 y^6<BR>\n" );
document.write( "D) 84x^2 y^7<BR>\n" );
document.write( "E) 36x^6 y^3 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #832245 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=832245\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> i believe it's selection B which is 36x^2y^7\r<BR>\n" );
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document.write( "the general formula is (x + y) ^ n = sum (c(n,k) * x^(n-k) * y^k) from k = 0 to n.\r<BR>\n" );
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document.write( "each term is c(n,k) * x^(n-k) * y^k\r<BR>\n" );
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document.write( "when n = 9, .....\r<BR>\n" );
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document.write( "the first term is c(9,0) * x^9 * y^0<BR>\n" );
document.write( "the second term is c(9,1) * x^8 * y^1<BR>\n" );
document.write( "the third term is c(9,2) * x^7 * y^2<BR>\n" );
document.write( "the fourth term is c(9,3) * x^6 * y^3<BR>\n" );
document.write( "the fifth term is c(9,4) * x^5 * y^4<BR>\n" );
document.write( "the sixth term is c(9,5) * x^4 * y^5<BR>\n" );
document.write( "the seventh term is c(9,6) * x^3 * y^6<BR>\n" );
document.write( "the eighth term is c(9,7) * x^2 * y^7<BR>\n" );
document.write( "the 9th term is c(9,8) * x^1 * y^8<BR>\n" );
document.write( "the 10th term is c(9,9) * x^0 * y^9\r<BR>\n" );
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document.write( "you are looking for the seventh term.\r<BR>\n" );
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document.write( "that term is c(9,6) * x^3 * y^6\r<BR>\n" );
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document.write( "c(9,6) = 9! / (6! * 3!) = (9*8*7*6!) = (6!*3!) = (9*8*7)/(3*2*1) = 84\r<BR>\n" );
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document.write( "the seventh term is therefore 84 * x^3 * y^6.\r<BR>\n" );
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document.write( "that would be selection A.\r<BR>\n" );
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document.write( "i confirmed with an online calculator.\r<BR>\n" );
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document.write( "the results of that calculator are shown below:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2022/112704.jpg\">\r<BR>\n" );
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document.write( "the terms are what's between the + signs.\r<BR>\n" );
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document.write( "the seventh term is therefore equal to 84x^3y^6\r<BR>\n" );
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document.write( "  </SPAN>\n" );
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