Solve -2x^{4}y^{3}+3/4x^{4}y^{4}-1/2x^{4}y^{3}):(-1/8x^2y+2x^2y)+(2/3x-frac{3}{5}x+x)(-2xy^2+frac{3}{2}xy^2)

$$- 2 x ^ { 4 } y ^ { 3 } + \frac { 3 } { 4 } x ^ { 4 } y ^ { 4 } - \frac { 1 } { 2 } x ^ { 4 } y ^ { 3 } ) : ( - \frac { 1 } { 8 } x ^ { 2 } y + 2 x ^ { 2 } y ) + ( \frac { 2 } { 3 } x - \frac { 3 } { 5 } x + x ) ( - 2 x y ^ { 2 } + \frac { 3 } { 2 } x y ^ { 2 } )$$

Factor

$$\frac{\left(3y-10\right)y^{3}x^{4}}{4}$$

Solution Steps

Factor out \frac{1}{4}.

$$\frac{-8x^{4}y^{3}+3x^{4}y^{4}-2x^{4}y^{3}}{4}$$

Consider -8x^{4}y^{3}+3x^{4}y^{4}-2x^{4}y^{3}. Factor out x^{4}y^{3}.

$$x^{4}y^{3}\left(-10+3y\right)$$

Consider -8+3y-2. Multiply and combine like terms.

$$3y-10$$

Rewrite the complete factored expression.

$$\frac{x^{4}y^{3}\left(3y-10\right)}{4}$$

Evaluate

$$\frac{\left(3y-10\right)y^{3}x^{4}}{4}$$