Prove that (n+1)!-n! = n.n!?

Let n=1. Then 2 - 1 = 1 x 1 and your premise is true in at least one case.

Let n=2. Then 6 - 4 = 2 x 2 and your premise is true in at least two cases.

Study the given equation and see what you can do with it.

(n + 1)! - n! = n x n!
(n + 1)! = n x n! + n!
(n + 1)! = (n + 1)!