In the BINOMIAL EXPANSION of , x9y9 occurs at the term where: 

As such, 9 = 13  -  (r  -  1)              OR                4 = r  -  1

9 = 13  -  r + 1                                             5 = r

9  -  14 = - r

- 5 = - r

5 = r

With the coefficients on x and y in  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 

OR

With the coefficient on x and y being 1, the coefficient on the 5th term will be: 

FYI: The entire EXPANSION DOESN'T HAVE to be done, as one person decided to do!

What if  was the 24th or 25th term of the expansion? Do you think it'd be wise to do the entire expansion? Think about it! 

Answer by greenestamps(13203)   (Show Source): You can put this solution on YOUR website!
 


Since the coefficients of x and y are both 1, the coefficient of the x^9y^4 term in the expansion of (x+y)^13 is


 

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