\(3x^2-x=x\cdot3x-x\cdot1=x\left(3x-1\right)\)
\(2xy+y^2=y\cdot2x+y\cdot y=y\left(2x+y\right)\)
\(x^3-x^2y=x^2\cdot x-x^2\cdot y=x^2\left(x-y\right)\)
\(3x-3y=3\cdot x-3\cdot y=3\left(x-y\right)\)
\(y^3+8y=y\left(y^2+8\right)\)
\(x^3y+5x^2y=x^2y\cdot x+x^2y\cdot5=x^2y\left(x+5\right)\)
\(4x^2y-6xy^2\)
\(=2xy\cdot2x-2xy\cdot3y\)
=2xy(2x-3y)