document.write( "Question 604308: Please help me solve this equation for a binomial expansion:\r
\n" ); document.write( "\n" ); document.write( "Find the 5th term in the expansion of (2a - b)^9\r
\n" ); document.write( "\n" ); document.write( "Here is the work that I have done:\r
\n" ); document.write( "\n" ); document.write( "n = 9 k = 4
\n" ); document.write( "n-k = 5 x = 2a
\n" ); document.write( "y = -b\r
\n" ); document.write( "\n" ); document.write( "(9 over 4)(2a)^5 (-b)4 \r
\n" ); document.write( "\n" ); document.write( "The answer comes out as:\r
\n" ); document.write( "\n" ); document.write( "(126)(32a^5)(b^4)\r
\n" ); document.write( "\n" ); document.write( "How did they get 126 out of this problem? \n" ); document.write( "

Algebra.Com's Answer #381113 by jim_thompson5910(35256) $\"\"$ $\"About$

You can put this solution on YOUR website!
It turns out that the \"(9 over 4)\" refers to the combination 9 C 4, which is\r
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\n" ); document.write( "\n" ); document.write( "9 C 4 = (9!)/(4!(9-4)!) = (9*8*7*6*5!)/(4!5!) = (9*8*7*6)/(4*3*2*1) = 3024/24 = 126\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "So 9 C 4 = 126\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "They just used different notation to represent the same idea. Let me know if this makes sense. \n" ); document.write( "

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