Answer
$$-b $$
Work Step by Step
By substituting, we get the intermediate form $\frac{0}{0}$. So, by factorizing the numerator, we have
$$
\lim _{a \rightarrow b } \frac{a^2-2ab+2b^2}{a-b}=\lim _{a \rightarrow b } \frac{(a-b)(a-2b)}{a-b}\\
=\lim _{a \rightarrow b } a-2b =b-2b=-b.
$$
