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v\left(v+7\right)-w\left(v+7\right)
Do the grouping v^{2}+7v-vw-7w=\left(v^{2}+7v\right)+\left(-vw-7w\right), and factor out v in the first and -w in the second group.
\left(v+7\right)\left(v-w\right)
Factor out common term v+7 by using distributive property.