Factorise:ab2 + (a − 1)b − 1
We have:
$a b^{2}+(a-1) b-1=a b^{2}+b a-b-1$
$=\left(a b^{2}+b a\right)-(b+1)$
$=a b(b+1)-1(b+1)$
$=(b+1)(a b-1)$
$\therefore a b^{2}+(a-1) b-1=(b+1)(a b-1)$
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