Answer
False.
The statement could become true if we write:
$a^{2}+b^{2}$ can not be factored.
Work Step by Step
First step: adding 0 = ab-ab does not change the result (OK).
Second step: ERROR in factoring of the second group.
It should read:
$=a(a+b)-b(a-b)$
So the next step does not follow, since there is no common binomial to extract.
(no factorization possible)
