Induction I am reviewing the Induction lecture but get stuck

Induction

I am reviewing the Induction lecture but get stuck on step 2 and 3. Can someone tell me how does the \"2n+2\" in step 2 become \"(n+m)+(n-m+1)+1\" in step 3?

(BC = Base Case, IS = Inductive Step)

Solution

2n + 2 = ( n+m ) + ( n - m + 1 ) + 1

we can write 2n+2 as ( n+m ) + ( n - m + 1 ) + 1

if we open the brackets it is equivalent to 2n+2