Solve (1/2a^2)-(-1/4a^2-1/3ab+2/5b^2)

$$( \frac { 1 } { 2 } a ^ { 2 } ) - ( - \frac { 1 } { 4 } a ^ { 2 } - \frac { 1 } { 3 } a b + \frac { 2 } { 5 } b ^ { 2 } )$$

Evaluate

$$\frac{ab}{3}+\frac{3a^{2}}{4}-\frac{2b^{2}}{5}$$

Solution Steps

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

$$\frac{1}{2}a^{2}+\frac{1}{4}a^{2}+\frac{1}{3}ab-\frac{2}{5}b^{2}$$

Combine \frac{1}{2}a^{2} and \frac{1}{4}a^{2} to get \frac{3}{4}a^{2}.

$$\frac{3}{4}a^{2}+\frac{1}{3}ab-\frac{2}{5}b^{2}$$

Expand

$$\frac{ab}{3}+\frac{3a^{2}}{4}-\frac{2b^{2}}{5}$$

Solution Steps

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

$$\frac{1}{2}a^{2}+\frac{1}{4}a^{2}+\frac{1}{3}ab-\frac{2}{5}b^{2}$$

Combine \frac{1}{2}a^{2} and \frac{1}{4}a^{2} to get \frac{3}{4}a^{2}.

$$\frac{3}{4}a^{2}+\frac{1}{3}ab-\frac{2}{5}b^{2}$$