Solve a^{2}-2a^3+[3-3a^2-(a^3+1/2)]+3a^3-5/2=

$$a ^ { 2 } - 2 a ^ { 3 } + [ 3 - 3 a ^ { 2 } - ( a ^ { 3 } + \frac { 1 } { 2 } ) ] + 3 a ^ { 3 } - \frac { 5 } { 2 } =$$

Evaluate

$$-2a^{2}$$

Solution Steps

Combine a^{2} and -3a^{2} to get -2a^{2}.

$$-2a^{2}-2a^{3}+3-\left(a^{3}+\frac{1}{2}\right)+3a^{3}-\frac{5}{2}$$

To find the opposite of a^{3}+\frac{1}{2}, find the opposite of each term.

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

Combine -2a^{3} and -a^{3} to get -3a^{3}.

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

Subtract \frac{1}{2} from 3 to get \frac{5}{2}.

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

Combine -3a^{3} and 3a^{3} to get 0.

$$-2a^{2}+\frac{5}{2}-\frac{5}{2}$$

Subtract \frac{5}{2} from \frac{5}{2} to get 0.

$$-2a^{2}$$

Expand

$$-2a^{2}$$

Solution Steps

Combine a^{2} and -3a^{2} to get -2a^{2}.

$$-2a^{2}-2a^{3}+3-\left(a^{3}+\frac{1}{2}\right)+3a^{3}-\frac{5}{2}$$

To find the opposite of a^{3}+\frac{1}{2}, find the opposite of each term.

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

Combine -2a^{3} and -a^{3} to get -3a^{3}.

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

Subtract \frac{1}{2} from 3 to get \frac{5}{2}.

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

Combine -3a^{3} and 3a^{3} to get 0.

$$-2a^{2}+\frac{5}{2}-\frac{5}{2}$$

Subtract \frac{5}{2} from \frac{5}{2} to get 0.

$$-2a^{2}$$