Solve (1/2m^{4}n^{3}+4m^{3}n^{5}-2/3m^3n^2)div(-1/6m^3n^2)

$$( \frac { 1 } { 2 } m ^ { 4 } n ^ { 3 } + 4 m ^ { 3 } n ^ { 5 } - \frac { 2 } { 3 } m ^ { 3 } n ^ { 2 } ) \div ( - \frac { 1 } { 6 } m ^ { 3 } n ^ { 2 } )$$

Evaluate

$$4-24n^{3}-3mn$$

Short Solution Steps

Factor the expressions that are not already factored.

$$\frac{\frac{1}{6}n^{2}m^{3}\left(3mn+24n^{3}-4\right)}{-\frac{1}{6}n^{2}m^{3}}$$

Cancel out n^{2}m^{3} in both numerator and denominator.

$$\frac{\frac{1}{6}\left(3mn+24n^{3}-4\right)}{-\frac{1}{6}}$$

Expand the expression.

$$\frac{\frac{1}{2}mn+4n^{3}-\frac{2}{3}}{-\frac{1}{6}}$$

Divide \frac{1}{2}mn+4n^{3}-\frac{2}{3} by -\frac{1}{6} by multiplying \frac{1}{2}mn+4n^{3}-\frac{2}{3} by the reciprocal of -\frac{1}{6}.

$$\frac{\left(\frac{1}{2}mn+4n^{3}-\frac{2}{3}\right)\times 6}{-1}$$

Anything divided by -1 gives its opposite.

$$-\left(\frac{1}{2}mn+4n^{3}-\frac{2}{3}\right)\times 6$$

Use the distributive property to multiply \frac{1}{2}mn+4n^{3}-\frac{2}{3} by 6.

$$-\left(3mn+24n^{3}-4\right)$$

To find the opposite of 3mn+24n^{3}-4, find the opposite of each term.

$$-3mn-24n^{3}+4$$

Expand

$$4-24n^{3}-3mn$$

Short Solution Steps

Factor the expressions that are not already factored.

$$\frac{\frac{1}{6}n^{2}m^{3}\left(3mn+24n^{3}-4\right)}{-\frac{1}{6}n^{2}m^{3}}$$

Cancel out n^{2}m^{3} in both numerator and denominator.

$$\frac{\frac{1}{6}\left(3mn+24n^{3}-4\right)}{-\frac{1}{6}}$$

Expand the expression.

$$\frac{\frac{1}{2}mn+4n^{3}-\frac{2}{3}}{-\frac{1}{6}}$$

Divide \frac{1}{2}mn+4n^{3}-\frac{2}{3} by -\frac{1}{6} by multiplying \frac{1}{2}mn+4n^{3}-\frac{2}{3} by the reciprocal of -\frac{1}{6}.

$$\frac{\left(\frac{1}{2}mn+4n^{3}-\frac{2}{3}\right)\times 6}{-1}$$

Anything divided by -1 gives its opposite.

$$-\left(\frac{1}{2}mn+4n^{3}-\frac{2}{3}\right)\times 6$$

Use the distributive property to multiply \frac{1}{2}mn+4n^{3}-\frac{2}{3} by 6.

$$-\left(3mn+24n^{3}-4\right)$$

To find the opposite of 3mn+24n^{3}-4, find the opposite of each term.

$$-3mn-24n^{3}+4$$