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25x\left(3x^{2}+y^{2}-2\right)+8y\left(3x^{2}+y^{2}-2\right)
Do the grouping 75x^{3}+25xy^{2}-50x+24x^{2}y+8y^{3}-16y=\left(75x^{3}+25xy^{2}-50x\right)+\left(24x^{2}y+8y^{3}-16y\right), and factor out 25x in the first and 8y in the second group.
\left(3x^{2}+y^{2}-2\right)\left(25x+8y\right)
Factor out common term 3x^{2}+y^{2}-2 by using distributive property.