How to factorize $a^2-b^2-a+b+(a+b-1)^2$? The answer is $(a+b-1)(2a-1)$ but I have no idea how to get this answer.

$$a^2-b^2-a+b+(a+b-1)^2\Leftrightarrow (a-b)(a+b)-(a-b)+(a+b-1)^2\\\implies(a-b)(a+b-1)+(a+b-1)^2=\boxed{(a+b-1)(2a-1)}$$
