Solve (3a^{4}b^{2}+2/3a^{3}b^{3}+4a^2b^4):(-1/4a^2b^2)

$$( 3 a ^ { 4 } b ^ { 2 } + \frac { 2 } { 3 } a ^ { 3 } b ^ { 3 } + 4 a ^ { 2 } b ^ { 4 } ) : ( - \frac { 1 } { 4 } a ^ { 2 } b ^ { 2 } )$$

Evaluate

$$-\frac{8ab}{3}-12a^{2}-16b^{2}$$

Short Solution Steps

Factor the expressions that are not already factored.

$$\frac{\frac{1}{3}a^{2}b^{2}\left(9a^{2}+2ab+12b^{2}\right)}{-\frac{1}{4}a^{2}b^{2}}$$

Cancel out a^{2}b^{2} in both numerator and denominator.

$$\frac{\frac{1}{3}\left(9a^{2}+2ab+12b^{2}\right)}{-\frac{1}{4}}$$

Expand the expression.

$$\frac{3a^{2}+\frac{2}{3}ab+4b^{2}}{-\frac{1}{4}}$$

Divide 3a^{2}+\frac{2}{3}ab+4b^{2} by -\frac{1}{4} by multiplying 3a^{2}+\frac{2}{3}ab+4b^{2} by the reciprocal of -\frac{1}{4}.

$$\frac{\left(3a^{2}+\frac{2}{3}ab+4b^{2}\right)\times 4}{-1}$$

Anything divided by -1 gives its opposite.

$$-\left(3a^{2}+\frac{2}{3}ab+4b^{2}\right)\times 4$$

Use the distributive property to multiply 3a^{2}+\frac{2}{3}ab+4b^{2} by 4.

$$-\left(12a^{2}+\frac{8}{3}ab+16b^{2}\right)$$

To find the opposite of 12a^{2}+\frac{8}{3}ab+16b^{2}, find the opposite of each term.

$$-12a^{2}-\frac{8}{3}ab-16b^{2}$$

Expand

$$-\frac{8ab}{3}-12a^{2}-16b^{2}$$

Short Solution Steps

Factor the expressions that are not already factored.

$$\frac{\frac{1}{3}a^{2}b^{2}\left(9a^{2}+2ab+12b^{2}\right)}{-\frac{1}{4}a^{2}b^{2}}$$

Cancel out a^{2}b^{2} in both numerator and denominator.

$$\frac{\frac{1}{3}\left(9a^{2}+2ab+12b^{2}\right)}{-\frac{1}{4}}$$

Expand the expression.

$$\frac{3a^{2}+\frac{2}{3}ab+4b^{2}}{-\frac{1}{4}}$$

Divide 3a^{2}+\frac{2}{3}ab+4b^{2} by -\frac{1}{4} by multiplying 3a^{2}+\frac{2}{3}ab+4b^{2} by the reciprocal of -\frac{1}{4}.

$$\frac{\left(3a^{2}+\frac{2}{3}ab+4b^{2}\right)\times 4}{-1}$$

Anything divided by -1 gives its opposite.

$$-\left(3a^{2}+\frac{2}{3}ab+4b^{2}\right)\times 4$$

Use the distributive property to multiply 3a^{2}+\frac{2}{3}ab+4b^{2} by 4.

$$-\left(12a^{2}+\frac{8}{3}ab+16b^{2}\right)$$

To find the opposite of 12a^{2}+\frac{8}{3}ab+16b^{2}, find the opposite of each term.

$$-12a^{2}-\frac{8}{3}ab-16b^{2}$$