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u\left(v-3\right)-2\left(v-3\right)
Do the grouping vu-3u-2v+6=\left(vu-3u\right)+\left(-2v+6\right), and factor out u in the first and -2 in the second group.
\left(v-3\right)\left(u-2\right)
Factor out common term v-3 by using distributive property.