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