Solve 4x^{3}y^{2}*(-2xy^2)+(-2x^2y)*(-1/2xy)*3x^2y^2z

$$4 x ^ { 3 } y ^ { 2 } \cdot ( - 2 x y ^ { 2 } ) + ( - 2 x ^ { 2 } y ) \cdot ( - \frac { 1 } { 2 } x y ) \cdot 3 x ^ { 2 } y ^ { 2 } z$$

Factor

$$\left(3xz-8\right)x^{4}y^{4}$$

Solution Steps

Factor out 2x^{2}y.

$$2x^{2}y\left(-4xyxy^{2}+\frac{3xyx^{2}y^{2}z}{2}\right)$$

Consider -4x^{2}y^{3}+\frac{3}{2}zx^{3}y^{3}. Factor out \frac{1}{2}.

$$\frac{-8x^{2}y^{3}+3zx^{3}y^{3}}{2}$$

Consider -8x^{2}y^{3}+3zx^{3}y^{3}. Factor out x^{2}y^{3}.

$$x^{2}y^{3}\left(-8+3zx\right)$$

Rewrite the complete factored expression.

$$x^{2}yx^{2}y^{3}\left(-8+3zx\right)$$

Simplify. Polynomial x^{2} is not factored since it does not have any rational roots.

$$y\left(-8+3zx\right)x^{4}y^{3}$$

Evaluate

$$\left(3xz-8\right)\left(xy\right)^{4}$$