Solve (4a^{3}-7a^{4})-(7a^3+8a^2)-(2a^2+a^4)

$$( 4 a ^ { 3 } - 7 a ^ { 4 } ) - ( 7 a ^ { 3 } + 8 a ^ { 2 } ) - ( 2 a ^ { 2 } + a ^ { 4 } )$$

Evaluate

$$-a^{2}\left(8a^{2}+3a+10\right)$$

Solution Steps

To find the opposite of 7a^{3}+8a^{2}, find the opposite of each term.

$$4a^{3}-7a^{4}-7a^{3}-8a^{2}-\left(2a^{2}+a^{4}\right)$$

Combine 4a^{3} and -7a^{3} to get -3a^{3}.

$$-3a^{3}-7a^{4}-8a^{2}-\left(2a^{2}+a^{4}\right)$$

To find the opposite of 2a^{2}+a^{4}, find the opposite of each term.

$$-3a^{3}-7a^{4}-8a^{2}-2a^{2}-a^{4}$$

Combine -8a^{2} and -2a^{2} to get -10a^{2}.

$$-3a^{3}-7a^{4}-10a^{2}-a^{4}$$

Combine -7a^{4} and -a^{4} to get -8a^{4}.

$$-3a^{3}-8a^{4}-10a^{2}$$

Expand

$$-8a^{4}-3a^{3}-10a^{2}$$

Solution Steps

To find the opposite of 7a^{3}+8a^{2}, find the opposite of each term.

$$4a^{3}-7a^{4}-7a^{3}-8a^{2}-\left(2a^{2}+a^{4}\right)$$

Combine 4a^{3} and -7a^{3} to get -3a^{3}.

$$-3a^{3}-7a^{4}-8a^{2}-\left(2a^{2}+a^{4}\right)$$

To find the opposite of 2a^{2}+a^{4}, find the opposite of each term.

$$-3a^{3}-7a^{4}-8a^{2}-2a^{2}-a^{4}$$

Combine -8a^{2} and -2a^{2} to get -10a^{2}.

$$-3a^{3}-7a^{4}-10a^{2}-a^{4}$$

Combine -7a^{4} and -a^{4} to get -8a^{4}.

$$-3a^{3}-8a^{4}-10a^{2}$$