Solve -(a^2+1/2ab)+(-1/4ab+1/2b^2)+(-1/4ab-frac{1}{5}b^2)

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

Evaluate

$$-ab+\frac{3b^{2}}{10}-a^{2}$$

Solution Steps

To find the opposite of a^{2}+\frac{1}{2}ab, find the opposite of each term.

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

Combine -\frac{1}{2}ab and -\frac{1}{4}ab to get -\frac{3}{4}ab.

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

Combine -\frac{3}{4}ab and -\frac{1}{4}ab to get -ab.

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

Combine \frac{1}{2}b^{2} and -\frac{1}{5}b^{2} to get \frac{3}{10}b^{2}.

$$-a^{2}-ab+\frac{3}{10}b^{2}$$

Expand

$$-ab+\frac{3b^{2}}{10}-a^{2}$$

Solution Steps

To find the opposite of a^{2}+\frac{1}{2}ab, find the opposite of each term.

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

Combine -\frac{1}{2}ab and -\frac{1}{4}ab to get -\frac{3}{4}ab.

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

Combine -\frac{3}{4}ab and -\frac{1}{4}ab to get -ab.

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

Combine \frac{1}{2}b^{2} and -\frac{1}{5}b^{2} to get \frac{3}{10}b^{2}.

$$-a^{2}-ab+\frac{3}{10}b^{2}$$