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2x\left(y+1\right)+z\left(y+1\right)
Do the grouping 2xy+z+2x+yz=\left(2xy+2x\right)+\left(yz+z\right), and factor out 2x in the first and z in the second group.
\left(y+1\right)\left(2x+z\right)
Factor out common term y+1 by using distributive property.