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2x^{2}-y^{2}-3x\left(2x^{2}-y^{2}\right)
Do the grouping 2x^{2}-y^{2}-6x^{3}+3xy^{2}=\left(2x^{2}-y^{2}\right)+\left(-6x^{3}+3xy^{2}\right), and factor out -3x in -6x^{3}+3xy^{2}.
\left(2x^{2}-y^{2}\right)\left(1-3x\right)
Factor out common term 2x^{2}-y^{2} by using distributive property.