Solve (3x^{4}y^{2}+2/3x^{3}y^{3}+4x^2y^4):(-1/4x^2y^2)

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

Evaluate

$$-\frac{8xy}{3}-12x^{2}-16y^{2}$$

Short Solution Steps

Factor the expressions that are not already factored.

$$\frac{\frac{1}{3}x^{2}y^{2}\left(9x^{2}+2xy+12y^{2}\right)}{-\frac{1}{4}x^{2}y^{2}}$$

Cancel out x^{2}y^{2} in both numerator and denominator.

$$\frac{\frac{1}{3}\left(9x^{2}+2xy+12y^{2}\right)}{-\frac{1}{4}}$$

Expand the expression.

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

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

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

Anything divided by -1 gives its opposite.

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

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

$$-\left(12x^{2}+\frac{8}{3}xy+16y^{2}\right)$$

To find the opposite of 12x^{2}+\frac{8}{3}xy+16y^{2}, find the opposite of each term.

$$-12x^{2}-\frac{8}{3}xy-16y^{2}$$

Expand

$$-\frac{8xy}{3}-12x^{2}-16y^{2}$$

Short Solution Steps

Factor the expressions that are not already factored.

$$\frac{\frac{1}{3}x^{2}y^{2}\left(9x^{2}+2xy+12y^{2}\right)}{-\frac{1}{4}x^{2}y^{2}}$$

Cancel out x^{2}y^{2} in both numerator and denominator.

$$\frac{\frac{1}{3}\left(9x^{2}+2xy+12y^{2}\right)}{-\frac{1}{4}}$$

Expand the expression.

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

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

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

Anything divided by -1 gives its opposite.

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

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

$$-\left(12x^{2}+\frac{8}{3}xy+16y^{2}\right)$$

To find the opposite of 12x^{2}+\frac{8}{3}xy+16y^{2}, find the opposite of each term.

$$-12x^{2}-\frac{8}{3}xy-16y^{2}$$