Solve -1/3x^2+[xy-(2/3x^2+2xy)+2xy]-(2x^2+3xy)

$$- \frac { 1 } { 3 } x ^ { 2 } + [ x y - ( \frac { 2 } { 3 } x ^ { 2 } + 2 x y ) + 2 x y ] - ( 2 x ^ { 2 } + 3 x y )$$

Evaluate

$$-x\left(3x+2y\right)$$

Solution Steps

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

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

Combine -\frac{1}{3}x^{2} and -\frac{2}{3}x^{2} to get -x^{2}.

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

Combine xy and -2xy to get -xy.

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

Combine -xy and 2xy to get xy.

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

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

$$-x^{2}+xy-2x^{2}-3xy$$

Combine -x^{2} and -2x^{2} to get -3x^{2}.

$$-3x^{2}+xy-3xy$$

Combine xy and -3xy to get -2xy.

$$-3x^{2}-2xy$$

Expand

$$-3x^{2}-2xy$$

Solution Steps

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

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

Combine -\frac{1}{3}x^{2} and -\frac{2}{3}x^{2} to get -x^{2}.

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

Combine xy and -2xy to get -xy.

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

Combine -xy and 2xy to get xy.

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

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

$$-x^{2}+xy-2x^{2}-3xy$$

Combine -x^{2} and -2x^{2} to get -3x^{2}.

$$-3x^{2}+xy-3xy$$

Combine xy and -3xy to get -2xy.

$$-3x^{2}-2xy$$