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x^{2}\left(3x-4y\right)+y^{2}\left(3x-4y\right)
Do the grouping 3x^{3}-4x^{2}y+3xy^{2}-4y^{3}=\left(3x^{3}-4x^{2}y\right)+\left(3xy^{2}-4y^{3}\right), and factor out x^{2} in the first and y^{2} in the second group.
\left(3x-4y\right)\left(x^{2}+y^{2}\right)
Factor out common term 3x-4y by using distributive property.