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x\left(x+2y\right)-8\left(x+2y\right)
Do the grouping x^{2}+2xy-8x-16y=\left(x^{2}+2xy\right)+\left(-8x-16y\right), and factor out x in the first and -8 in the second group.
\left(x+2y\right)\left(x-8\right)
Factor out common term x+2y by using distributive property.