Solve (8a^3+7a^2-9a)-(3a^3-2a^2-2a)

$$( 8 a ^ { 3 } + 7 a ^ { 2 } - 9 a ) - ( 3 a ^ { 3 } - 2 a ^ { 2 } - 2 a )$$

Evaluate

$$a\left(5a^{2}+9a-7\right)$$

Solution Steps

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

$$8a^{3}+7a^{2}-9a-3a^{3}+2a^{2}+2a$$

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

$$5a^{3}+7a^{2}-9a+2a^{2}+2a$$

Combine 7a^{2} and 2a^{2} to get 9a^{2}.

$$5a^{3}+9a^{2}-9a+2a$$

Combine -9a and 2a to get -7a.

$$5a^{3}+9a^{2}-7a$$

Expand

$$5a^{3}+9a^{2}-7a$$

Solution Steps

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

$$8a^{3}+7a^{2}-9a-3a^{3}+2a^{2}+2a$$

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

$$5a^{3}+7a^{2}-9a+2a^{2}+2a$$

Combine 7a^{2} and 2a^{2} to get 9a^{2}.

$$5a^{3}+9a^{2}-9a+2a$$

Combine -9a and 2a to get -7a.

$$5a^{3}+9a^{2}-7a$$