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Question 1116770: Find the Coefficient of X^n in the expansion of (4-x)^4n
Answer by KMST(5328)   (Show Source):
You can put this solution on YOUR website! Expanding the binomial power   
we get  terms.
Each term is a product of
a combinatorial number,
a power of  ,
and a power of  ,
where the sum of exponents adds up to  ,
and the combinatorial number is combinations of
taking as many at a time as one of the exponents.
For the term in  , we get  , multiplied by
combinations of taking  or at a time, which is  either way.
For the term in  , we get  , multiplied by
combinations of taking  (or  ) at a time.
You may represent combinations of taking (or ) at a time by symbols such as
 , or as  ,
, but that combinatorial number taking or ,
is    either way.
So, the coefficient of  is
 
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