Solve (4x^{2}+2y^{2}-3/4)-(-5x^2+3/2y^2+1/4)+(x^2-1/3y^2

$$( 4 x ^ { 2 } + 2 y ^ { 2 } - \frac { 3 } { 4 } ) - ( - 5 x ^ { 2 } + \frac { 3 } { 2 } y ^ { 2 } + \frac { 1 } { 4 } ) + ( x ^ { 2 } - \frac { 1 } { 3 } y ^ { 2 }$$

Evaluate

$$\frac{y^{2}}{6}+10x^{2}-1$$

Solution Steps

To find the opposite of -5x^{2}+\frac{3}{2}y^{2}+\frac{1}{4}, find the opposite of each term.

$$4x^{2}+2y^{2}-\frac{3}{4}+5x^{2}-\frac{3}{2}y^{2}-\frac{1}{4}+x^{2}-\frac{1}{3}y^{2}$$

Combine 4x^{2} and 5x^{2} to get 9x^{2}.

$$9x^{2}+2y^{2}-\frac{3}{4}-\frac{3}{2}y^{2}-\frac{1}{4}+x^{2}-\frac{1}{3}y^{2}$$

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

$$9x^{2}+\frac{1}{2}y^{2}-\frac{3}{4}-\frac{1}{4}+x^{2}-\frac{1}{3}y^{2}$$

Subtract \frac{1}{4} from -\frac{3}{4} to get -1.

$$9x^{2}+\frac{1}{2}y^{2}-1+x^{2}-\frac{1}{3}y^{2}$$

Combine 9x^{2} and x^{2} to get 10x^{2}.

$$10x^{2}+\frac{1}{2}y^{2}-1-\frac{1}{3}y^{2}$$

Combine \frac{1}{2}y^{2} and -\frac{1}{3}y^{2} to get \frac{1}{6}y^{2}.

$$10x^{2}+\frac{1}{6}y^{2}-1$$

Expand

$$\frac{y^{2}}{6}+10x^{2}-1$$

Solution Steps

To find the opposite of -5x^{2}+\frac{3}{2}y^{2}+\frac{1}{4}, find the opposite of each term.

$$4x^{2}+2y^{2}-\frac{3}{4}+5x^{2}-\frac{3}{2}y^{2}-\frac{1}{4}+x^{2}-\frac{1}{3}y^{2}$$

Combine 4x^{2} and 5x^{2} to get 9x^{2}.

$$9x^{2}+2y^{2}-\frac{3}{4}-\frac{3}{2}y^{2}-\frac{1}{4}+x^{2}-\frac{1}{3}y^{2}$$

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

$$9x^{2}+\frac{1}{2}y^{2}-\frac{3}{4}-\frac{1}{4}+x^{2}-\frac{1}{3}y^{2}$$

Subtract \frac{1}{4} from -\frac{3}{4} to get -1.

$$9x^{2}+\frac{1}{2}y^{2}-1+x^{2}-\frac{1}{3}y^{2}$$

Combine 9x^{2} and x^{2} to get 10x^{2}.

$$10x^{2}+\frac{1}{2}y^{2}-1-\frac{1}{3}y^{2}$$

Combine \frac{1}{2}y^{2} and -\frac{1}{3}y^{2} to get \frac{1}{6}y^{2}.

$$10x^{2}+\frac{1}{6}y^{2}-1$$