document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1002539>Question 1002539</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Consider the expansion of (x+y)^n.    thanks!\r<BR>\n" );
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document.write( "1. How many terms does the expression contain?<BR>\n" );
document.write( "2. What is the exponent of x in the first term?<BR>\n" );
document.write( "3. What is the exponent of y in the first term?<BR>\n" );
document.write( "4. What is the sum of the exponents in any term of the expansion ?\r<BR>\n" );
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document.write( "Show work please, thanks </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #619408 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=619408\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> # 1\r<BR>\n" );
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document.write( "If n = 1, there are 2 terms since (x+y)^n = (x+y)^1 = x+y<BR>\n" );
document.write( "If n = 2, there are 3 terms since (x+y)^n = (x+y)^2 = x^2+2xy+y^2<BR>\n" );
document.write( "If n = 3, there are 4 terms since (x+y)^n = (x+y)^3 = x^3+3x^2y+3xy^2+y^3<BR>\n" );
document.write( "and so on<BR>\n" );
document.write( "The pattern continues. For any positive integer n, there are n+1 terms in (x+y)^n\r<BR>\n" );
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document.write( "# 2\r<BR>\n" );
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document.write( "If n = 1, then (x+y)^n = (x+y)^1 = x+y<BR>\n" );
document.write( "First term is x = x^1\r<BR>\n" );
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document.write( "If n = 2, then (x+y)^n = (x+y)^2 = x^2+2xy+y^2<BR>\n" );
document.write( "First term is x^2\r<BR>\n" );
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document.write( "If n = 3, then (x+y)^n = (x+y)^3 = x^3+3x^2y+3xy^2+y^3<BR>\n" );
document.write( "First term is x^3\r<BR>\n" );
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document.write( "I'm sure you see the pattern here as well\r<BR>\n" );
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document.write( "The first term of (x+y)^n is x^n. There are NO y terms in the first term\r<BR>\n" );
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document.write( "The exponent for the x in the first term is n\r<BR>\n" );
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document.write( "# 3\r<BR>\n" );
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document.write( "See problem #2 above. The first term is x^n which is really the same as x^n*y^0. So the exponent for y in the first term is 0\r<BR>\n" );
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document.write( "# 4\r<BR>\n" );
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document.write( "The sum of exponents of any monomial term is always n\r<BR>\n" );
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document.write( "Take a look at (x+y)^3 = x^3+3x^2y+3xy^2+y^3, where n = 3 in this case\r<BR>\n" );
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document.write( "Then focus on a term like 3x^2y. This term is the same as 3x^2*y^1. The exponents are 2 and 1 which add to 2+1 = 3 which is the value of n.<BR>\n" );
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