SOLUTION: Show that (n+1)! -3(n!) + (n-1)! = (n-1)!(n-1)²

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Question 856887: Show that (n+1)! -3(n!) + (n-1)! = (n-1)!(n-1)²
Answer by Edwin McCravy(20055) About Me  (Show Source):
You can put this solution on YOUR website!
Show that (n+1)! - 3(n!) + (n-1)! = (n-1)!(n-1)²
By the definition of factorial, we know that:

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

n! = (n)(n-1)!

So the left side becomes:

(n+1)(n)(n-1)! - 3(n)(n-1)! + (n-1)!

Factor out (n-1)!

(n-1)![(n+1)n - 3n + 1)

Remove the parentheses inside the brackets:

(n-1)![n² + n - 3n + 1]

Combine like terms:

(n-1)![n²-2n+1]

Factor the trinomial in the bracket:

(n-1)!(n-1)(n-1)

Write (n-1)(n-1) and (n-1)²

(n-1)!(n-1)²  

Edwin