How do you simplify $n!-(n-1)!$

Question

I'm unsure how to simplify the expression $n!-(n-1)!$.

Working as well as the final answer would be preferable.

Answer 1

Hint: $n! = n \cdot (n - 1)!$.

Answer 2

$n!$ is defined inductively by $0!=1$ and $n!=n\cdot(n-1)!$ for $n\geqslant 1$. Hence $$n! - (n-1)! = n\cdot(n-1)! - (n-1)! = (n-1)(n-1)! $$

Answer 3

$$n!-(n-1)!=n(n-1)!-(n-1)!=(n-1)!\left( n-1 \right) $$