Factorise:

We have:

$a b^{2}+(a-1) b-1=a b^{2}+b a-b-1$

$=\left(a b^{2}+b a\right)-(b+1)$

$=a b(b+1)-1(b+1)$

$=(b+1)(a b-1)$

$\therefore a b^{2}+(a-1) b-1=(b+1)(a b-1)$