Factorize ab² + (a – 1)b – 1.

As there is no common factor among all terms, to factorize ab² + (a – 1)b – 1 we rewrite it by expanding the middle term

⇒ ab² + (a – 1)b – 1 = ab² + ab – b – 1

We can write ab² = a × b × b and –b = (–1) × b

⇒ ab² + ab – b – 1 = a × b × b + a × b + (–1) × b + (–1)

Observe that ab is common for the first two terms and (–1) is common for the next two terms.

⇒ ab² + ab – b – 1 = ab(b + 1) + (–1)(b + 1)

Now, (b + 1) is the common term.

∴ ab² + (a – 1)b – 1 = (ab – 1)(b + 1)

Hence, the factors of ab² + (a – 1)b – 1 are (ab – 1) and (b + 1).