Expand Factorials refer to the process of simplifying or expanding a factorial expression. In this case, we are looking at two specific expressions: (n-2)! and (n-n')!. These expressions involve the use of factorials, which are mathematical functions denoted by an exclamation mark (!) and used to calculate the product of a given number and all the positive integers less than it.
To expand (n-2)!, we can use the formula n! = n(n-1)(n-2)...3*2*1. Similarly, to expand (n-n')!, we can use the formula n! = n(n-1)(n-2)...(n-n'+1)(n-n').
Expanding factorials can help simplify complex mathematical expressions and make them easier to solve or understand. It is also used in various fields of science, such as probability and statistics, to calculate the number of possible outcomes or combinations.
Yes, (n-2)! and (n-n')! can be further simplified using algebraic manipulation. For example, we can factor out common terms or use properties of factorials, such as n! = n*(n-1)! to simplify the expressions.
Yes, there are some special cases to consider when expanding (n-2)! and (n-n')!. For example, when n = 2, (n-2)! becomes 0! which is equal to 1. When n = n', (n-n')! becomes 0! which is also equal to 1.