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y^{2}\left(a-4b\right)-2x\left(a-4b\right)
Do the grouping ay^{2}-4by^{2}-2ax+8bx=\left(ay^{2}-4by^{2}\right)+\left(-2ax+8bx\right), and factor out y^{2} in the first and -2x in the second group.
\left(a-4b\right)\left(y^{2}-2x\right)
Factor out common term a-4b by using distributive property.