Answer
$(a-2b)(2a-b)$
Work Step by Step
Using the factoring of trinomials in the form $ax^2+bx+c,$ the $\text{
expression
}$
\begin{array}{l}\require{cancel}
2a^2-5ab+2b^2
\end{array} has $ac=
2(2)=4
$ and $b=
-5
.$
The two numbers with a product of $c$ and a sum of $b$ are $\left\{
-4,-1
\right\}.$ Using these $2$ numbers to decompose the middle term of the trinomial expression above results to
\begin{array}{l}\require{cancel}
2a^2-4ab-1ab+2b^2
.\end{array}
Grouping the first and second terms and the third and fourth terms, the given expression is equivalent to
\begin{array}{l}\require{cancel}
(2a^2-4ab)-(ab-2b^2)
.\end{array}
Factoring the $GCF$ in each group results to
\begin{array}{l}\require{cancel}
2a(a-2b)-b(a-2b)
.\end{array}
Factoring the $GCF=
(a-2b)
$ of the entire expression above results to
\begin{array}{l}\require{cancel}
(a-2b)(2a-b)
.\end{array}