Solve (4x^3y-xy^3+3/2xy)div(-1/2xy)

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

Evaluate

$$-8x^{2}+2y^{2}-3$$

Short Solution Steps

Factor the expressions that are not already factored.

$$\frac{\frac{1}{2}xy\left(8x^{2}-2y^{2}+3\right)}{-\frac{1}{2}xy}$$

Cancel out xy in both numerator and denominator.

$$\frac{\frac{1}{2}\left(8x^{2}-2y^{2}+3\right)}{-\frac{1}{2}}$$

Expand the expression.

$$\frac{4x^{2}-y^{2}+\frac{3}{2}}{-\frac{1}{2}}$$

Divide 4x^{2}-y^{2}+\frac{3}{2} by -\frac{1}{2} by multiplying 4x^{2}-y^{2}+\frac{3}{2} by the reciprocal of -\frac{1}{2}.

$$\frac{\left(4x^{2}-y^{2}+\frac{3}{2}\right)\times 2}{-1}$$

Anything divided by -1 gives its opposite.

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

Use the distributive property to multiply 4x^{2}-y^{2}+\frac{3}{2} by 2.

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

To find the opposite of 8x^{2}-2y^{2}+3, find the opposite of each term.

$$-8x^{2}+2y^{2}-3$$

Expand

$$-8x^{2}+2y^{2}-3$$

Short Solution Steps

Factor the expressions that are not already factored.

$$\frac{\frac{1}{2}xy\left(8x^{2}-2y^{2}+3\right)}{-\frac{1}{2}xy}$$

Cancel out xy in both numerator and denominator.

$$\frac{\frac{1}{2}\left(8x^{2}-2y^{2}+3\right)}{-\frac{1}{2}}$$

Expand the expression.

$$\frac{4x^{2}-y^{2}+\frac{3}{2}}{-\frac{1}{2}}$$

Divide 4x^{2}-y^{2}+\frac{3}{2} by -\frac{1}{2} by multiplying 4x^{2}-y^{2}+\frac{3}{2} by the reciprocal of -\frac{1}{2}.

$$\frac{\left(4x^{2}-y^{2}+\frac{3}{2}\right)\times 2}{-1}$$

Anything divided by -1 gives its opposite.

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

Use the distributive property to multiply 4x^{2}-y^{2}+\frac{3}{2} by 2.

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

To find the opposite of 8x^{2}-2y^{2}+3, find the opposite of each term.

$$-8x^{2}+2y^{2}-3$$