Solve 3x-[2a^{2}-(2a-3x^2)]+a^2-[2a-(a^2-3x^2)]

$$3 x - [ 2 a ^ { 2 } - ( 2 a - 3 x ^ { 2 } ) ] + a ^ { 2 } - [ 2 a - ( a ^ { 2 } - 3 x ^ { 2 } ) ]$$

Evaluate

$$3x\left(1-2x\right)$$

Solution Steps

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

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

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

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

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

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

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

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

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

$$3x-a^{2}+2a-3x^{2}-2a+a^{2}-3x^{2}$$

Combine 2a and -2a to get 0.

$$3x-a^{2}-3x^{2}+a^{2}-3x^{2}$$

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

$$3x-3x^{2}-3x^{2}$$

Combine -3x^{2} and -3x^{2} to get -6x^{2}.

$$3x-6x^{2}$$

Expand

$$3x-6x^{2}$$

Solution Steps

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

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

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

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

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

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

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

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

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

$$3x-a^{2}+2a-3x^{2}-2a+a^{2}-3x^{2}$$

Combine 2a and -2a to get 0.

$$3x-a^{2}-3x^{2}+a^{2}-3x^{2}$$

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

$$3x-3x^{2}-3x^{2}$$

Combine -3x^{2} and -3x^{2} to get -6x^{2}.

$$3x-6x^{2}$$