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

$$\frac{ 1 }{ 2 } { x }^{ 2 } (-4y)-(- \frac{ 7 }{ 6 } { x }^{ 2 } y)(xy)- \frac{ 1 }{ 3 } x(- { x }^{ 2 } y) \frac{ 5 }{ 2 } y- \frac{ x }{ 4 } (-2xy)$$

Factor

$$\frac{yx^{2}\left(4xy-3\right)}{2}$$

Solution Steps

Factor out \frac{1}{6}.

$$\frac{-12x^{2}y+7x^{2}yxy+5xx^{2}yy+3xxy}{6}$$

Consider -12x^{2}y+7x^{3}y^{2}+5x^{3}y^{2}+3yx^{2}. Factor out x^{2}y.

$$x^{2}y\left(-9+12xy\right)$$

Consider -12+7xy+5xy+3. Multiply and combine like terms.

$$12xy-9$$

Consider 12xy-9. Factor out 3.

$$3\left(4xy-3\right)$$

Rewrite the complete factored expression.

$$\frac{x^{2}y\left(4xy-3\right)}{2}$$

Simplify.

$$\frac{y\left(4xy-3\right)x^{2}}{2}$$

Evaluate

$$\frac{yx^{2}\left(4xy-3\right)}{2}$$