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2\left(a+2\right)+b\left(a+2\right)
Do the grouping 2a+4+ab+2b=\left(2a+4\right)+\left(ab+2b\right), and factor out 2 in the first and b in the second group.
\left(a+2\right)\left(2+b\right)
Factor out common term a+2 by using distributive property.