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x\left(z+10\right)+y\left(z+10\right)
Do the grouping xz+10x+yz+10y=\left(xz+10x\right)+\left(yz+10y\right), and factor out x in the first and y in the second group.
\left(z+10\right)\left(x+y\right)
Factor out common term z+10 by using distributive property.