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.

$$(a+b-1)^2=a^2+b^2+1-2a-2b+2ab$$
$$\implies a^2-b^2-a+b+(a+b-1)^2=2a(a+b)-\{2a+(a+b)\}+1$$
$$ =2a\{a+b-1\}-\{a+b-1\}=?$$
