document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=925477>Question 925477</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Use Pascal's triangle to expand the expression.<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 #561562 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20850)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathLover1><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=MathLover1><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=561562\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Use Pascal's Triangle to expand each binomial.<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<BR>\n" );
document.write( "1 10 45 120 210 252 210 120 45 10 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( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2By%29%5E8 ALIGN=MIDDLE  ALT=\"%28x%2By%29%5E8\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Nineth raw of the triangle gives,COEFFIECIENTS OF THE EXPANSION.\r<BR>\n" );
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document.write( "That is, <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1 ALIGN=MIDDLE  ALT=\"1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+8 ALIGN=MIDDLE  ALT=\"+8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+28 ALIGN=MIDDLE  ALT=\"+28\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+56 ALIGN=MIDDLE  ALT=\"+56\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+70 ALIGN=MIDDLE  ALT=\"+70\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+56 ALIGN=MIDDLE  ALT=\"+56\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+28 ALIGN=MIDDLE  ALT=\"+28\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+8 ALIGN=MIDDLE  ALT=\"+8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+1 ALIGN=MIDDLE  ALT=\"+1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\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( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E8 ALIGN=MIDDLE  ALT=\"x%5E8\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E7+%2A+y%5E1 ALIGN=MIDDLE  ALT=\"x%5E7+%2A+y%5E1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E6%2A+y%5E2 ALIGN=MIDDLE  ALT=\"x%5E6%2A+y%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E5+%2A+y%5E3 ALIGN=MIDDLE  ALT=\"x%5E5+%2A+y%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E4+%2A+y%5E4 ALIGN=MIDDLE  ALT=\"x%5E4+%2A+y%5E4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E3+%2A+y%5E5 ALIGN=MIDDLE  ALT=\"x%5E3+%2A+y%5E5\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2Ax%5E6 ALIGN=MIDDLE  ALT=\"x%5E2%2Ax%5E6\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E1%2Ax%5E7 ALIGN=MIDDLE  ALT=\"x%5E1%2Ax%5E7\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5E8%7D%7D%5D%0D%0A%0D%0A%28power+of+the+first+term+will+decrease+while+power+of+second+term+will+increase+till+it+is+%7B%7B%7B8 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >)\r<BR>\n" );
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document.write( "Since here it is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x+%2B+y%29 ALIGN=MIDDLE  ALT=\"%28x+%2B+y%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, the sign of the all  terms will be   positive,\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x+%2B+y%29%5E8=+++1x%5E8%2B+8x%5E7%2Ay%5E1%2B+28x%5E6%2Ay%5E2%2B56x%5E5%2Ay%5E3%2B+70x%5E4%2Ay%5E4%2B+56x%5E3%2Ay%5E5%2B+28x%5E2%2Ay%5E6%2B8x%2Ay%5E7%2By%5E8 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x+%2B+y%29%5E8=++x%5E8%2B8x%5E7%2Ay%2B28x%5E6%2Ay%5E2%2B56x%5E5%2Ay%5E3%2B70x%5E4%2Ay%5E4%2B56x%5E3%2Ay%5E5%2B28x%5E2%2Ay%5E6%2B8x%2A+y%5E7%2By%5E8 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\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( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );