Solve -(4a^{5}+3a^{4}+6)+(-7a^4+8-3a^5)-(5a^4-2a^3

$$- ( 4 a ^ { 5 } + 3 a ^ { 4 } + 6 ) + ( - 7 a ^ { 4 } + 8 - 3 a ^ { 5 } ) - ( 5 a ^ { 4 } - 2 a ^ { 3 }$$

Evaluate

$$2+2a^{3}-15a^{4}-7a^{5}$$

Solution Steps

To find the opposite of 4a^{5}+3a^{4}+6, find the opposite of each term.

$$-4a^{5}-3a^{4}-6-7a^{4}+8-3a^{5}-\left(5a^{4}-2a^{3}\right)$$

Combine -3a^{4} and -7a^{4} to get -10a^{4}.

$$-4a^{5}-10a^{4}-6+8-3a^{5}-\left(5a^{4}-2a^{3}\right)$$

Add -6 and 8 to get 2.

$$-4a^{5}-10a^{4}+2-3a^{5}-\left(5a^{4}-2a^{3}\right)$$

Combine -4a^{5} and -3a^{5} to get -7a^{5}.

$$-7a^{5}-10a^{4}+2-\left(5a^{4}-2a^{3}\right)$$

To find the opposite of 5a^{4}-2a^{3}, find the opposite of each term.

$$-7a^{5}-10a^{4}+2-5a^{4}+2a^{3}$$

Combine -10a^{4} and -5a^{4} to get -15a^{4}.

$$-7a^{5}-15a^{4}+2+2a^{3}$$

Expand

$$2+2a^{3}-15a^{4}-7a^{5}$$

Solution Steps

To find the opposite of 4a^{5}+3a^{4}+6, find the opposite of each term.

$$-4a^{5}-3a^{4}-6-7a^{4}+8-3a^{5}-\left(5a^{4}-2a^{3}\right)$$

Combine -3a^{4} and -7a^{4} to get -10a^{4}.

$$-4a^{5}-10a^{4}-6+8-3a^{5}-\left(5a^{4}-2a^{3}\right)$$

Add -6 and 8 to get 2.

$$-4a^{5}-10a^{4}+2-3a^{5}-\left(5a^{4}-2a^{3}\right)$$

Combine -4a^{5} and -3a^{5} to get -7a^{5}.

$$-7a^{5}-10a^{4}+2-\left(5a^{4}-2a^{3}\right)$$

To find the opposite of 5a^{4}-2a^{3}, find the opposite of each term.

$$-7a^{5}-10a^{4}+2-5a^{4}+2a^{3}$$

Combine -10a^{4} and -5a^{4} to get -15a^{4}.

$$-7a^{5}-15a^{4}+2+2a^{3}$$