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\frac{6x^{2}y-2xy^{2}+xy}{2}
Factor out \frac{1}{2}.
xy\left(6x-2y+1\right)
Consider 6x^{2}y-2xy^{2}+xy. Factor out xy.
\frac{xy\left(6x-2y+1\right)}{2}
Rewrite the complete factored expression.