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4\left(x^{3}y+2yx\right)
Factor out 4.
xy\left(x^{2}+2\right)
Consider x^{3}y+2yx. Factor out xy.
4xy\left(x^{2}+2\right)
Rewrite the complete factored expression. Polynomial x^{2}+2 is not factored since it does not have any rational roots.