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ab\left(b+1\right)+b+1
Do the grouping ab^{2}+ab+b+1=\left(ab^{2}+ab\right)+\left(b+1\right), and factor out ab in ab^{2}+ab.
\left(b+1\right)\left(ab+1\right)
Factor out common term b+1 by using distributive property.