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2x\left(-4y+1\right)-\left(-4y+1\right)
Do the grouping 2x+4y-8xy-1=\left(-8xy+2x\right)+\left(-1\right), and factor out 2x in the first and -1 in the second group.
\left(-4y+1\right)\left(2x-1\right)
Factor out common term -4y+1 by using distributive property.