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9x\left(x+y\right)-8\left(x+y\right)
Do the grouping 9x^{2}+9xy-8x-8y=\left(9x^{2}+9xy\right)+\left(-8x-8y\right), and factor out 9x in the first and -8 in the second group.
\left(x+y\right)\left(9x-8\right)
Factor out common term x+y by using distributive property.