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

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

Evaluate

$$a\left(11a^{2}+4a-6\right)$$

Solution Steps

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

$$3a^{2}+4a^{3}-6a-4a^{2}+3a^{3}+4a^{3}+5a^{2}$$

Combine 3a^{2} and -4a^{2} to get -a^{2}.

$$-a^{2}+4a^{3}-6a+3a^{3}+4a^{3}+5a^{2}$$

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

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

Combine 7a^{3} and 4a^{3} to get 11a^{3}.

$$-a^{2}+11a^{3}-6a+5a^{2}$$

Combine -a^{2} and 5a^{2} to get 4a^{2}.

$$4a^{2}+11a^{3}-6a$$

Expand

$$11a^{3}+4a^{2}-6a$$

Solution Steps

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

$$3a^{2}+4a^{3}-6a-4a^{2}+3a^{3}+4a^{3}+5a^{2}$$

Combine 3a^{2} and -4a^{2} to get -a^{2}.

$$-a^{2}+4a^{3}-6a+3a^{3}+4a^{3}+5a^{2}$$

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

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

Combine 7a^{3} and 4a^{3} to get 11a^{3}.

$$-a^{2}+11a^{3}-6a+5a^{2}$$

Combine -a^{2} and 5a^{2} to get 4a^{2}.

$$4a^{2}+11a^{3}-6a$$