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