document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=63563>Question 63563</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Use Pascal's Triangle to expand each binomial.<BR>\n" );
document.write( "(a-b)^6 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #44272 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=44272\">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( "(a-b)^6\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)^6\r<BR>\n" );
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document.write( "Seventh raw of the triangle gives,COEFFIECIENTS OF THE EXPANSION.\r<BR>\n" );
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document.write( "That is, 1 6 15 20 15 6 1\r<BR>\n" );
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document.write( "And the variable terms  will come like this,\r<BR>\n" );
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document.write( "x^6\r<BR>\n" );
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document.write( "x^5 * y^1\r<BR>\n" );
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document.write( "x^4* y^2\r<BR>\n" );
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document.write( "x^3 * y^3\r<BR>\n" );
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document.write( "x^2 * y^4\r<BR>\n" );
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document.write( "x^1 * y^5\r<BR>\n" );
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document.write( "y^6\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 6.)\r<BR>\n" );
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document.write( "Since here it is (x - 6), the sign of the term will be alternatively positive and negative like this,\r<BR>\n" );
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document.write( "+, -, + , -, +, -, +, - , +, ...................\r<BR>\n" );
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document.write( "(x-y)^6=   1x^6+ 6x^5 y^1+ 15x^4 y^2+20x^3 y^3+ 15x^2 y^4+ 6x^1 y^5+ 1y^6\r<BR>\n" );
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document.write( "which is the  answer to your question.\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" );