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

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

Evaluate

$$8-2b$$

Solution Steps

To find the opposite of a^{2}+b-1, find the opposite of each term.

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

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

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

Combine 2b and -b to get b.

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

Add 4 and 1 to get 5.

$$2a^{2}+b+5-\left(a^{2}+2b-1\right)-\left(a^{2}+b-2\right)$$

To find the opposite of a^{2}+2b-1, find the opposite of each term.

$$2a^{2}+b+5-a^{2}-2b+1-\left(a^{2}+b-2\right)$$

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

$$a^{2}+b+5-2b+1-\left(a^{2}+b-2\right)$$

Combine b and -2b to get -b.

$$a^{2}-b+5+1-\left(a^{2}+b-2\right)$$

Add 5 and 1 to get 6.

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

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

$$a^{2}-b+6-a^{2}-b+2$$

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

$$-b+6-b+2$$

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

$$-2b+6+2$$

Add 6 and 2 to get 8.

$$-2b+8$$

Expand

$$8-2b$$

Solution Steps

To find the opposite of a^{2}+b-1, find the opposite of each term.

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

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

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

Combine 2b and -b to get b.

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

Add 4 and 1 to get 5.

$$2a^{2}+b+5-\left(a^{2}+2b-1\right)-\left(a^{2}+b-2\right)$$

To find the opposite of a^{2}+2b-1, find the opposite of each term.

$$2a^{2}+b+5-a^{2}-2b+1-\left(a^{2}+b-2\right)$$

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

$$a^{2}+b+5-2b+1-\left(a^{2}+b-2\right)$$

Combine b and -2b to get -b.

$$a^{2}-b+5+1-\left(a^{2}+b-2\right)$$

Add 5 and 1 to get 6.

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

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

$$a^{2}-b+6-a^{2}-b+2$$

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

$$-b+6-b+2$$

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

$$-2b+6+2$$

Add 6 and 2 to get 8.

$$-2b+8$$