Evaluation of an expression

Question

I have difficulties to evaluate this expression to the desired result. (It is a proof based on mathematical induction, left = right)

$(k+1)!-1+(k+1)*(k+1)! = (k+2)!-1$

Answer 1

This can be done my factoring out the common terms. Note that

$$\color{blue}{(k+1)!}(k+1)+\color{blue}{(k+1)!}\times 1-1=\color{blue}{(k+1)!}(k+1+1)-1=(k+2)(k+1)!-1$$

But $(k+2)(k+1)!=(k+2)!$

Thus $(k+1)!-1+(k+1)*(k+1)! = (k+2)!-1$.