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4x\left(x+y\right)-7\left(x+y\right)
Do the grouping 4x^{2}+4xy-7x-7y=\left(4x^{2}+4xy\right)+\left(-7x-7y\right), and factor out 4x in the first and -7 in the second group.
\left(x+y\right)\left(4x-7\right)
Factor out common term x+y by using distributive property.