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