Solve m^2+11/3m-1/4m^3-(7/4m^3-21/3m)-m^2-m-(-frac{2}{3}m)

$$m ^ { 2 } + \frac { 11 } { 3 } m - \frac { 1 } { 4 } m ^ { 3 } - ( \frac { 7 } { 4 } m ^ { 3 } - \frac { 21 } { 3 } m ) - m ^ { 2 } - m - ( - \frac { 2 } { 3 } m )$$

Evaluate

$$-2m^{3}+\frac{31m}{3}$$

Solution Steps

Divide 21 by 3 to get 7.

$$m^{2}+\frac{11}{3}m-\frac{1}{4}m^{3}-\left(\frac{7}{4}m^{3}-7m\right)-m^{2}-m-\left(-\frac{2}{3}m\right)$$

To find the opposite of \frac{7}{4}m^{3}-7m, find the opposite of each term.

$$m^{2}+\frac{11}{3}m-\frac{1}{4}m^{3}-\frac{7}{4}m^{3}+7m-m^{2}-m-\left(-\frac{2}{3}m\right)$$

Combine -\frac{1}{4}m^{3} and -\frac{7}{4}m^{3} to get -2m^{3}.

$$m^{2}+\frac{11}{3}m-2m^{3}+7m-m^{2}-m-\left(-\frac{2}{3}m\right)$$

Combine \frac{11}{3}m and 7m to get \frac{32}{3}m.

$$m^{2}+\frac{32}{3}m-2m^{3}-m^{2}-m-\left(-\frac{2}{3}m\right)$$

Combine m^{2} and -m^{2} to get 0.

$$\frac{32}{3}m-2m^{3}-m-\left(-\frac{2}{3}m\right)$$

Combine \frac{32}{3}m and -m to get \frac{29}{3}m.

$$\frac{29}{3}m-2m^{3}-\left(-\frac{2}{3}m\right)$$

The opposite of -\frac{2}{3}m is \frac{2}{3}m.

$$\frac{29}{3}m-2m^{3}+\frac{2}{3}m$$

Combine \frac{29}{3}m and \frac{2}{3}m to get \frac{31}{3}m.

$$\frac{31}{3}m-2m^{3}$$

Expand

$$-2m^{3}+\frac{31m}{3}$$

Solution Steps

Divide 21 by 3 to get 7.

$$m^{2}+\frac{11}{3}m-\frac{1}{4}m^{3}-\left(\frac{7}{4}m^{3}-7m\right)-m^{2}-m-\left(-\frac{2}{3}m\right)$$

To find the opposite of \frac{7}{4}m^{3}-7m, find the opposite of each term.

$$m^{2}+\frac{11}{3}m-\frac{1}{4}m^{3}-\frac{7}{4}m^{3}+7m-m^{2}-m-\left(-\frac{2}{3}m\right)$$

Combine -\frac{1}{4}m^{3} and -\frac{7}{4}m^{3} to get -2m^{3}.

$$m^{2}+\frac{11}{3}m-2m^{3}+7m-m^{2}-m-\left(-\frac{2}{3}m\right)$$

Combine \frac{11}{3}m and 7m to get \frac{32}{3}m.

$$m^{2}+\frac{32}{3}m-2m^{3}-m^{2}-m-\left(-\frac{2}{3}m\right)$$

Combine m^{2} and -m^{2} to get 0.

$$\frac{32}{3}m-2m^{3}-m-\left(-\frac{2}{3}m\right)$$

Combine \frac{32}{3}m and -m to get \frac{29}{3}m.

$$\frac{29}{3}m-2m^{3}-\left(-\frac{2}{3}m\right)$$

The opposite of -\frac{2}{3}m is \frac{2}{3}m.

$$\frac{29}{3}m-2m^{3}+\frac{2}{3}m$$

Combine \frac{29}{3}m and \frac{2}{3}m to get \frac{31}{3}m.

$$\frac{31}{3}m-2m^{3}$$