Solve [(-1/2x)^{3}(-3xy^{2})^{2}-7/8x(xy)^{4}]-{(xy)^2[1/3x(-xy)^2+1/4x^3y^2]-frac{5}{6}x

$$[ ( - \frac { 1 } { 2 } x ) ^ { 3 } ( - 3 x y ^ { 2 } ) ^ { 2 } - \frac { 7 } { 8 } x ( x y ) ^ { 4 } ] - \{ ( x y ) ^ { 2 } [ \frac { 1 } { 3 } x ( - x y ) ^ { 2 } + \frac { 1 } { 4 } x ^ { 3 } y ^ { 2 } ] - \frac { 5 } { 6 } x$$

Factor

$$-\frac{31y^{4}x^{5}}{12}+\frac{5x}{6}$$

Solution Steps

Factor out \frac{1}{8}.

$$\frac{-9x^{3}\left(xy^{2}\right)^{2}-7x\left(xy\right)^{4}-8\left(xy\right)^{2}\left(\frac{x\left(-xy\right)^{2}}{3}+\frac{x^{3}y^{2}}{4}\right)-\frac{5x}{6}}{8}$$

Evaluate

$$-\frac{31x\left(xy\right)^{4}}{12}+\frac{5x}{6}$$