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x\left(a+b+2\right)-\left(a+b+2\right)
Do the grouping 2x-2+bx-b+ax-a=\left(ax+bx+2x\right)+\left(-a-b-2\right), and factor out x in the first and -1 in the second group.
\left(a+b+2\right)\left(x-1\right)
Factor out common term a+b+2 by using distributive property.