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7x^{2}\left(2x-1\right)+y\left(2x-1\right)
Do the grouping 14x^{3}-7x^{2}+2xy-y=\left(14x^{3}-7x^{2}\right)+\left(2xy-y\right), and factor out 7x^{2} in the first and y in the second group.
\left(2x-1\right)\left(7x^{2}+y\right)
Factor out common term 2x-1 by using distributive property.