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\frac{1}{2}x-2x+\frac{2}{3}y^{2}-\frac{3}{2}x+\frac{1}{3}y^{2}
Use the distributive property to multiply -2 by x-\frac{1}{3}y^{2}.
-\frac{3}{2}x+\frac{2}{3}y^{2}-\frac{3}{2}x+\frac{1}{3}y^{2}
Combine \frac{1}{2}x and -2x to get -\frac{3}{2}x.
-3x+\frac{2}{3}y^{2}+\frac{1}{3}y^{2}
Combine -\frac{3}{2}x and -\frac{3}{2}x to get -3x.
-3x+y^{2}
Combine \frac{2}{3}y^{2} and \frac{1}{3}y^{2} to get y^{2}.
\frac{1}{2}x-2x+\frac{2}{3}y^{2}-\frac{3}{2}x+\frac{1}{3}y^{2}
Use the distributive property to multiply -2 by x-\frac{1}{3}y^{2}.
-\frac{3}{2}x+\frac{2}{3}y^{2}-\frac{3}{2}x+\frac{1}{3}y^{2}
Combine \frac{1}{2}x and -2x to get -\frac{3}{2}x.
-3x+\frac{2}{3}y^{2}+\frac{1}{3}y^{2}
Combine -\frac{3}{2}x and -\frac{3}{2}x to get -3x.
-3x+y^{2}
Combine \frac{2}{3}y^{2} and \frac{1}{3}y^{2} to get y^{2}.