Solve (2+8a^{2}-a^{3})+(2a^3-3a^2-8)-(12-7a^3+5a^2)

$$( 2 + 8 a ^ { 2 } - a ^ { 3 } ) + ( 2 a ^ { 3 } - 3 a ^ { 2 } - 8 ) - ( 12 - 7 a ^ { 3 } + 5 a ^ { 2 } )$$

Evaluate

$$8a^{3}-18$$

Solution Steps

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

$$2+8a^{2}+a^{3}-3a^{2}-8-\left(12-7a^{3}+5a^{2}\right)$$

Combine 8a^{2} and -3a^{2} to get 5a^{2}.

$$2+5a^{2}+a^{3}-8-\left(12-7a^{3}+5a^{2}\right)$$

Subtract 8 from 2 to get -6.

$$-6+5a^{2}+a^{3}-\left(12-7a^{3}+5a^{2}\right)$$

To find the opposite of 12-7a^{3}+5a^{2}, find the opposite of each term.

$$-6+5a^{2}+a^{3}-12+7a^{3}-5a^{2}$$

Subtract 12 from -6 to get -18.

$$-18+5a^{2}+a^{3}+7a^{3}-5a^{2}$$

Combine a^{3} and 7a^{3} to get 8a^{3}.

$$-18+5a^{2}+8a^{3}-5a^{2}$$

Combine 5a^{2} and -5a^{2} to get 0.

$$-18+8a^{3}$$

Expand

$$8a^{3}-18$$

Solution Steps

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

$$2+8a^{2}+a^{3}-3a^{2}-8-\left(12-7a^{3}+5a^{2}\right)$$

Combine 8a^{2} and -3a^{2} to get 5a^{2}.

$$2+5a^{2}+a^{3}-8-\left(12-7a^{3}+5a^{2}\right)$$

Subtract 8 from 2 to get -6.

$$-6+5a^{2}+a^{3}-\left(12-7a^{3}+5a^{2}\right)$$

To find the opposite of 12-7a^{3}+5a^{2}, find the opposite of each term.

$$-6+5a^{2}+a^{3}-12+7a^{3}-5a^{2}$$

Subtract 12 from -6 to get -18.

$$-18+5a^{2}+a^{3}+7a^{3}-5a^{2}$$

Combine a^{3} and 7a^{3} to get 8a^{3}.

$$-18+5a^{2}+8a^{3}-5a^{2}$$

Combine 5a^{2} and -5a^{2} to get 0.

$$-18+8a^{3}$$