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-\frac{1}{3}x^{2}+xy-\frac{2}{3}x^{2}-2xy+2xy-\left(2x^{2}+3xy\right)
To find the opposite of \frac{2}{3}x^{2}+2xy, find the opposite of each term.
-x^{2}+xy-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-\left(2x^{2}+3xy\right)
Combine xy and -2xy to get -xy.
-x^{2}+xy-\left(2x^{2}+3xy\right)
Combine -xy and 2xy to get xy.
-x^{2}+xy-2x^{2}-3xy
To find the opposite of 2x^{2}+3xy, find the opposite of each term.
-3x^{2}+xy-3xy
Combine -x^{2} and -2x^{2} to get -3x^{2}.
-3x^{2}-2xy
Combine xy and -3xy to get -2xy.
-\frac{1}{3}x^{2}+xy-\frac{2}{3}x^{2}-2xy+2xy-\left(2x^{2}+3xy\right)
To find the opposite of \frac{2}{3}x^{2}+2xy, find the opposite of each term.
-x^{2}+xy-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-\left(2x^{2}+3xy\right)
Combine xy and -2xy to get -xy.
-x^{2}+xy-\left(2x^{2}+3xy\right)
Combine -xy and 2xy to get xy.
-x^{2}+xy-2x^{2}-3xy
To find the opposite of 2x^{2}+3xy, find the opposite of each term.
-3x^{2}+xy-3xy
Combine -x^{2} and -2x^{2} to get -3x^{2}.
-3x^{2}-2xy
Combine xy and -3xy to get -2xy.