Solve -(2/3ab+c)-(5/9ab+3c-1/4c^2)+(11/9ab+frac{1}{2}c-frac{1}{8}c)

$$- ( \frac { 2 } { 3 } a b + c ) - ( \frac { 5 } { 9 } a b + 3 c - \frac { 1 } { 4 } c ^ { 2 } ) + ( \frac { 11 } { 9 } a b + \frac { 1 } { 2 } c - \frac { 1 } { 8 } c )$$

Evaluate

$$\frac{c\left(2c-29\right)}{8}$$

Solution Steps

To find the opposite of \frac{2}{3}ab+c, find the opposite of each term.

$$-\frac{2}{3}ab-c-\left(\frac{5}{9}ab+3c-\frac{1}{4}c^{2}\right)+\frac{11}{9}ab+\frac{1}{2}c-\frac{1}{8}c$$

To find the opposite of \frac{5}{9}ab+3c-\frac{1}{4}c^{2}, find the opposite of each term.

$$-\frac{2}{3}ab-c-\frac{5}{9}ab-3c+\frac{1}{4}c^{2}+\frac{11}{9}ab+\frac{1}{2}c-\frac{1}{8}c$$

Combine -\frac{2}{3}ab and -\frac{5}{9}ab to get -\frac{11}{9}ab.

$$-\frac{11}{9}ab-c-3c+\frac{1}{4}c^{2}+\frac{11}{9}ab+\frac{1}{2}c-\frac{1}{8}c$$

Combine -c and -3c to get -4c.

$$-\frac{11}{9}ab-4c+\frac{1}{4}c^{2}+\frac{11}{9}ab+\frac{1}{2}c-\frac{1}{8}c$$

Combine -\frac{11}{9}ab and \frac{11}{9}ab to get 0.

$$-4c+\frac{1}{4}c^{2}+\frac{1}{2}c-\frac{1}{8}c$$

Combine -4c and \frac{1}{2}c to get -\frac{7}{2}c.

$$-\frac{7}{2}c+\frac{1}{4}c^{2}-\frac{1}{8}c$$

Combine -\frac{7}{2}c and -\frac{1}{8}c to get -\frac{29}{8}c.

$$-\frac{29}{8}c+\frac{1}{4}c^{2}$$

Expand

$$\frac{c^{2}}{4}-\frac{29c}{8}$$

Solution Steps

To find the opposite of \frac{2}{3}ab+c, find the opposite of each term.

$$-\frac{2}{3}ab-c-\left(\frac{5}{9}ab+3c-\frac{1}{4}c^{2}\right)+\frac{11}{9}ab+\frac{1}{2}c-\frac{1}{8}c$$

To find the opposite of \frac{5}{9}ab+3c-\frac{1}{4}c^{2}, find the opposite of each term.

$$-\frac{2}{3}ab-c-\frac{5}{9}ab-3c+\frac{1}{4}c^{2}+\frac{11}{9}ab+\frac{1}{2}c-\frac{1}{8}c$$

Combine -\frac{2}{3}ab and -\frac{5}{9}ab to get -\frac{11}{9}ab.

$$-\frac{11}{9}ab-c-3c+\frac{1}{4}c^{2}+\frac{11}{9}ab+\frac{1}{2}c-\frac{1}{8}c$$

Combine -c and -3c to get -4c.

$$-\frac{11}{9}ab-4c+\frac{1}{4}c^{2}+\frac{11}{9}ab+\frac{1}{2}c-\frac{1}{8}c$$

Combine -\frac{11}{9}ab and \frac{11}{9}ab to get 0.

$$-4c+\frac{1}{4}c^{2}+\frac{1}{2}c-\frac{1}{8}c$$

Combine -4c and \frac{1}{2}c to get -\frac{7}{2}c.

$$-\frac{7}{2}c+\frac{1}{4}c^{2}-\frac{1}{8}c$$

Combine -\frac{7}{2}c and -\frac{1}{8}c to get -\frac{29}{8}c.

$$-\frac{29}{8}c+\frac{1}{4}c^{2}$$