document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=63552>Question 63552</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Use Pascal's Triangle to expand each binomial.<BR>\n" );
document.write( "(x+y)^8 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #44265 by </B><A HREF=/tutors/aboutme.mpl?userid=praseenakos@yahoo.com><B>praseenakos@yahoo.com(507)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=praseenakos@yahoo.com><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=praseenakos@yahoo.com><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=44265\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> QUESTION;\r<BR>\n" );
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document.write( "Use Pascal's Triangle to expand each binomial.<BR>\n" );
document.write( "(x+y)^8\r<BR>\n" );
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document.write( "ANSWER:\r<BR>\n" );
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document.write( "Pascal's Triangle. \r<BR>\n" );
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document.write( "It is a triangle of numbers,  which is given below:\r<BR>\n" );
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document.write( "1<BR>\n" );
document.write( "1 1<BR>\n" );
document.write( "1 2 1<BR>\n" );
document.write( "1 3 3 1<BR>\n" );
document.write( "1 4 6 4 1<BR>\n" );
document.write( "1 5 10 10 5 1<BR>\n" );
document.write( "1 6 15 20 15 6 1<BR>\n" );
document.write( "1 7 21 35 35 21 7 1<BR>\n" );
document.write( "1 8 28 56 70 56 28 8 1<BR>\n" );
document.write( "1 9 36 84 126 126 84 36 9 1\r<BR>\n" );
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document.write( "Each number in the triangle is the sum of two above. For example, the 6 on line 5 is the sum of the pair of 3's above. So the next line is\r<BR>\n" );
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document.write( "1, 10 (1 + 9), 45 (9 + 36), 120 (36 + 84), etc.\r<BR>\n" );
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document.write( "Study these numbers and see if you can figure what the next line should be before reading on . . .\r<BR>\n" );
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document.write( "Your question.\r<BR>\n" );
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document.write( "(x+y)^8\r<BR>\n" );
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document.write( "Here we have to expand the 8th power.\r<BR>\n" );
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document.write( "Ninth raw in Pascal's triangle gives the coefficient of the terms in the resulting expansion.\r<BR>\n" );
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document.write( "that means, the coeffients are,  1 8 28 56 70 56 28 8 1\r<BR>\n" );
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document.write( "Now write the variable part like this,\r<BR>\n" );
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document.write( "x^8\r<BR>\n" );
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document.write( "x^7 * y\r<BR>\n" );
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document.write( "x^6 * y^2\r<BR>\n" );
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document.write( "x^5 * y^3\r<BR>\n" );
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document.write( "x^4 * y^4\r<BR>\n" );
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document.write( "x^3 * y^5\r<BR>\n" );
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document.write( "x^2 * y^6\r<BR>\n" );
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document.write( "x^1 * y^7\r<BR>\n" );
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document.write( "y^8  \r<BR>\n" );
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document.write( "(power of the first term will decrease while power of second term will increase till it is 8.)\r<BR>\n" );
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document.write( "(x+y)^8 =   1x^8+ 8x^7 y^1+ 28x^6 y^2 + 56 x^5 y^3+ 70x^4 y^4+56x^3y^5  + <BR>\n" );
document.write( "28x^2 y^6+ 8x^1 y^7+ 1x^8\r<BR>\n" );
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document.write( "    = x^8+ 8x^7 y^1+ 28x^6 y^2 + 56 x^5 y^3+ 70x^4 y^4+56x^3y^5  + <BR>\n" );
document.write( "28x^2 y^6+ 8x^1 y^7+ x^8\r<BR>\n" );
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document.write( "Hope you understood.\r<BR>\n" );
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document.write( "Regards.\r<BR>\n" );
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document.write( "Praseenakos@yahoo.co.in\r<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );