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x\left(z+7\right)+y\left(z+7\right)
Do the grouping 7x+xz+7y+yz=\left(7x+xz\right)+\left(7y+yz\right), and factor out x in the first and y in the second group.
\left(z+7\right)\left(x+y\right)
Factor out common term z+7 by using distributive property.