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a\left(b-1\right)-\left(b-1\right)
Do the grouping ab-a-b+1=\left(ab-a\right)+\left(-b+1\right), and factor out a in the first and -1 in the second group.
\left(b-1\right)\left(a-1\right)
Factor out common term b-1 by using distributive property.