Solve (1+4a^2)-(3b-2a^2)+[2b-(3a^2-b)+a^2]-(2b+2)=

$$( 1 + 4 a ^ { 2 } ) - ( 3 b - 2 a ^ { 2 } ) + [ 2 b - ( 3 a ^ { 2 } - b ) + a ^ { 2 } ] - ( 2 b + 2 ) =$$

Evaluate

$$4a^{2}-2b-1$$

Solution Steps

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

$$1+4a^{2}-3b+2a^{2}+2b-\left(3a^{2}-b\right)+a^{2}-\left(2b+2\right)$$

Combine 4a^{2} and 2a^{2} to get 6a^{2}.

$$1+6a^{2}-3b+2b-\left(3a^{2}-b\right)+a^{2}-\left(2b+2\right)$$

Combine -3b and 2b to get -b.

$$1+6a^{2}-b-\left(3a^{2}-b\right)+a^{2}-\left(2b+2\right)$$

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

$$1+6a^{2}-b-3a^{2}+b+a^{2}-\left(2b+2\right)$$

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

$$1+3a^{2}-b+b+a^{2}-\left(2b+2\right)$$

Combine -b and b to get 0.

$$1+3a^{2}+a^{2}-\left(2b+2\right)$$

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

$$1+4a^{2}-\left(2b+2\right)$$

To find the opposite of 2b+2, find the opposite of each term.

$$1+4a^{2}-2b-2$$

Subtract 2 from 1 to get -1.

$$-1+4a^{2}-2b$$

Expand

$$4a^{2}-2b-1$$

Solution Steps

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

$$1+4a^{2}-3b+2a^{2}+2b-\left(3a^{2}-b\right)+a^{2}-\left(2b+2\right)$$

Combine 4a^{2} and 2a^{2} to get 6a^{2}.

$$1+6a^{2}-3b+2b-\left(3a^{2}-b\right)+a^{2}-\left(2b+2\right)$$

Combine -3b and 2b to get -b.

$$1+6a^{2}-b-\left(3a^{2}-b\right)+a^{2}-\left(2b+2\right)$$

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

$$1+6a^{2}-b-3a^{2}+b+a^{2}-\left(2b+2\right)$$

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

$$1+3a^{2}-b+b+a^{2}-\left(2b+2\right)$$

Combine -b and b to get 0.

$$1+3a^{2}+a^{2}-\left(2b+2\right)$$

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

$$1+4a^{2}-\left(2b+2\right)$$

To find the opposite of 2b+2, find the opposite of each term.

$$1+4a^{2}-2b-2$$

Subtract 2 from 1 to get -1.

$$-1+4a^{2}-2b$$