Question

prove: the difference of two even integers is even. 2n - 2m = ?(n - m) = even

Explanation:

Step1: Factor out common term

Factor 2 from $2n-2m$.
$2n - 2m = 2(n - m)$

Step2: Verify evenness

Since $n,m$ are integers, $n-m$ is integer. A number multiplied by 2 is even.
$2\times(\text{integer}) = \text{even number}$

Answer:

2