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u\left(2v-1\right)+2\left(2v-1\right)
Do the grouping 2uv-u+4v-2=\left(2uv-u\right)+\left(4v-2\right), and factor out u in the first and 2 in the second group.
\left(2v-1\right)\left(u+2\right)
Factor out common term 2v-1 by using distributive property.