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v\left(u-3\right)-4\left(u-3\right)
Do the grouping uv-3v-4u+12=\left(uv-3v\right)+\left(-4u+12\right), and factor out v in the first and -4 in the second group.
\left(u-3\right)\left(v-4\right)
Factor out common term u-3 by using distributive property.