Solve 3(a^2+a+1)+2(a^2+2a-2)-(a^2+3a-3)

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

Evaluate

$$4a^{2}+4a+2$$

Solution Steps

Use the distributive property to multiply 3 by a^{2}+a+1.

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

Use the distributive property to multiply 2 by a^{2}+2a-2.

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

Combine 3a^{2} and 2a^{2} to get 5a^{2}.

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

Combine 3a and 4a to get 7a.

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

Subtract 4 from 3 to get -1.

$$5a^{2}+7a-1-\left(a^{2}+3a-3\right)$$

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

$$5a^{2}+7a-1-a^{2}-3a+3$$

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

$$4a^{2}+7a-1-3a+3$$

Combine 7a and -3a to get 4a.

$$4a^{2}+4a-1+3$$

Add -1 and 3 to get 2.

$$4a^{2}+4a+2$$

Expand

$$4a^{2}+4a+2$$

Solution Steps

Use the distributive property to multiply 3 by a^{2}+a+1.

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

Use the distributive property to multiply 2 by a^{2}+2a-2.

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

Combine 3a^{2} and 2a^{2} to get 5a^{2}.

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

Combine 3a and 4a to get 7a.

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

Subtract 4 from 3 to get -1.

$$5a^{2}+7a-1-\left(a^{2}+3a-3\right)$$

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

$$5a^{2}+7a-1-a^{2}-3a+3$$

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

$$4a^{2}+7a-1-3a+3$$

Combine 7a and -3a to get 4a.

$$4a^{2}+4a-1+3$$

Add -1 and 3 to get 2.

$$4a^{2}+4a+2$$