Factorial simplification with fractions I am attempting to simplify the expression

gnatopoditw 2022-06-25 Answered
Factorial simplification with fractions
I am attempting to simplify the expression
( x + y 2 ) ! ( x y 2 ) ! y !
I'm familiar with expanding expressions like
y ! = ( y ) ( y 1 ) ( y 2 )
but I have not encountered this before, a fraction inside a factorial. Am I looking for something like
( x + y 2 ) ! = ( x + y 2 ) ( ( x 1 ) + ( y 1 ) 1 ) ,
and this is where I am stuck. Any help would be great.
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Answers (2)

tennispopj8
Answered 2022-06-26 Author has 20 answers
( x + y 2 ) ! = ( x + y 2 ) ( x + y 2 1 ) ( x + y 2 2 ) 3 2 1
Your original expression is about as simplified as it's going to get. It is only defined if x , y are both even, or both odd.

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Lucille Cummings
Answered 2022-06-27 Author has 5 answers
The expression is of the form
a ! b ! ( a b ) ! ,
provided x and y share the same parity, of course. Now this simplifies (?) to
( a b ) b ! .

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