document.write( "Question 1137744: determine the coefficient of x^9 y^4 in the binomial expansion of (x + y)^13 power \n" ); document.write( "
Algebra.Com's Answer #755624 by MathTherapy(10555)\"\" \"About 
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\n" ); document.write( "determine the coefficient of x^9 y^4 in the binomial expansion of (x + y)^13 power
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In the BINOMIAL EXPANSION of \"%28x+%2B+y%29%5E13\", x9y9 occurs at the term where: 
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document.write( "As such, 9 = 13  -  (r  -  1)              OR                4 = r  -  1
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document.write( "9 = 13  -  r + 1                                             5 = r
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document.write( "9  -  14 = - r
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document.write( "- 5 = - r
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document.write( "5 = r
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document.write( "With the coefficients on x and y in \"%28x+%2B+y%29%5E13\" being 1, the coefficient on the 5th term, when expanded, will be the value in the 5th COLUMN of the 13th ROW of Pascal’s triangle, which is \"highlight_green%28715%29\"
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document.write( "OR
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document.write( "With the coefficient on x and y being 1, the coefficient on the 5th term will be: 
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document.write( "FYI: The entire EXPANSION DOESN'T HAVE to be done, as one person decided to do!
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document.write( "What if \"x%5E9y%5E4\" was the 24th or 25th term of the expansion? Do you think it'd be wise to do the entire expansion? Think about it! \n" );
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