document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=23449>Question 23449</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 1). Solve for r<BR>\n" );
document.write( "    7!/(7-r)! = 840\r<BR>\n" );
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document.write( "2). Expand (a-2)^5 using the binomal theoren.<BR>\n" );
document.write( "    (Is there a shorter way to expand this without multiplying (a-2) 5 times<BR>\n" );
document.write( "     and writing out a lot of numbers?)<BR>\n" );
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document.write( "a) a^5-8a^4+16a^3-24a^2+24a-32<BR>\n" );
document.write( "b) a^5-10a^4+40a^3-80a^2+80a-32\r<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #12239 by </B><A HREF=/tutors/aboutme.mpl?userid=venugopalramana><B>venugopalramana(3286)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=venugopalramana><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.geocities.com/venugopalramana/FREE_MATHS_ASSISTANCE.html valign=middle><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=12239\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 1). Solve for r<BR>\n" );
document.write( "7!/(7-r)! = 840 <BR>\n" );
document.write( "7!/840=(7-R)!<BR>\n" );
document.write( "7*6*5*4*3*2*1/840=(7-R)!<BR>\n" );
document.write( "3*2*1=(7-R)!=3!<BR>\n" );
document.write( "7-R=3<BR>\n" );
document.write( "R=7-3=4\r<BR>\n" );
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document.write( "2). Expand (a-2)^5 using the binomal theoren.<BR>\n" );
document.write( "(Is there a shorter way to expand this without multiplying (a-2) 5 times<BR>\n" );
document.write( "and writing out a lot of numbers?)<BR>\n" );
document.write( "BINOMIAL THEOREM...<BR>\n" );
document.write( "(X+A)^N=(NC0)*X^N+(NC1)*(X^(N-1))*(A)+(NC2)*(X^(N-2))*(A^2)+...+(NCR)X^(N-R)*(A^R)+.......+(NCN)*A^N<BR>\n" );
document.write( "FOR NUMERICAL PROBLEMS YOU CAN USE THIS ORAL CALCULATION<BR>\n" );
document.write( "(X+A)^5=1*X^5+(5*1/1)X^4*A+(5*4/2)X^3*A^2+(10*3/3)X^2*A^3+(10*2/4)X^1*A^4+(5*1/5)A^5<BR>\n" );
document.write( "POWERS...START WITH X^5...OR...=X^5*A^0=...GO ON REDUCING BY 1 FOR EACH TERM<BR>\n" );
document.write( "THE POWER OF X AND INCREASING BY 1 THE POWER OF A...THAT IS X^5,X^4*A,X^3*A^2....TILL YOU END WITH X^0*A^5=A^5<BR>\n" );
document.write( "NOW COEFFICIENTS ARE CALCULATED AS SHOWN ABOVE  AND EXPLAINED BELOW.<BR>\n" );
document.write( "1.START WITH 1 FOR THE 1ST.TERM<BR>\n" );
document.write( "2...2ND.TERM....MULTIPLY THE COEFFICIENT OF PREVIOUS TERM (1)WITH POWER OF X IN THAT (5)AND DIVIDE BY THE NUMBER OF TERMS OVER OR WRITTEN ALREADY(1)=5*1/1=5 IS THE COEFFICIENT OF NEXT OR NEW TERM<BR>\n" );
document.write( "3.....3RD.TERM..SAME WAY REPEAT...MULTIPLY THE COEFFICIENT OF PREVIOUS TERM (5)WITH POWER OF X IN THAT (4)AND DIVIDE BY THE NUMBER OF TERMS OVER OR WRITTEN ALREADY(2)=5*4/2=10 IS THE COEFFICIENT OF NEXT OR NEW TERM<BR>\n" );
document.write( "4..THE WORKING FOR OTHERS IS SHOWN ABOVE IN BRACKETS..\r<BR>\n" );
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document.write( "NOW YOU CAN DO YOUR PROBLEM USING <BR>\n" );
document.write( "X=a AND A=-2\r<BR>\n" );
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document.write( "a) a^5-8a^4+16a^3-24a^2+24a-32<BR>\n" );
document.write( "b) a^5-10a^4+40a^3-80a^2+80a-32 \r<BR>\n" );
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