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6\left(x+y\right)+x\left(x+y\right)
Do the grouping 6x+6y+x^{2}+xy=\left(6x+6y\right)+\left(x^{2}+xy\right), and factor out 6 in the first and x in the second group.
\left(x+y\right)\left(6+x\right)
Factor out common term x+y by using distributive property.