Direct Proofs

Write clear and complete direct proofs for each of the following mathematical statements.
(1) If x | a and x | b, then x | (a^2 - b^2).
Proof. Assume that x | a and x | b, then   we know that a = xm, and b = xn for some integers m and n. Now
a^2 - b^2 = (xm)^2 - (xm)^2
               = x^2m^2 - x^2n^2
               = x(xm^2 - xn^2)
               = xq
where q = (xm^2 - xn^2) is an integer. Therefore x| (a^2 - b^2).

QED