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x\left(x+2\right)+2y\left(x+2\right)
Do the grouping x^{2}+2x+2xy+4y=\left(x^{2}+2x\right)+\left(2xy+4y\right), and factor out x in the first and 2y in the second group.
\left(x+2\right)\left(x+2y\right)
Factor out common term x+2 by using distributive property.