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v\left(u+2\right)-x\left(u+2\right)
Do the grouping uv+2v-ux-2x=\left(uv+2v\right)+\left(-ux-2x\right), and factor out v in the first and -x in the second group.
\left(u+2\right)\left(v-x\right)
Factor out common term u+2 by using distributive property.