Simplifying a proof statement. Trying to simplify a the following equation:
Prove that if n is an even integer and m an an odd integer, then $(n + 2)^2 - (m - 1)^2$ is even
So this is what I have so far:
If n is an integer
      then n = 2k where k is some integer and
     m = 2j + 1 where j is some integer.
Then: $(2k + 2)^2 - (2j + 1-1)^2$ 
     =$(2k + 2)^2 - (2j)^2$ 
I really need to get the expression down to 2(..) where (..) is some integer to prove the statement.

You are so close:
$(2k+2)^2−(2j)^2\\
4[(k+1)^2 - j^2]$
