Solve (5a^2+2a+1)-4(3-8a+2a^2)+(3a^2-a)

$$( 5 a ^ { 2 } + 2 a + 1 ) - 4 ( 3 - 8 a + 2 a ^ { 2 } ) + ( 3 a ^ { 2 } - a )$$

Evaluate

$$33a-11$$

Solution Steps

Use the distributive property to multiply -4 by 3-8a+2a^{2}.

$$5a^{2}+2a+1-12+32a-8a^{2}+3a^{2}-a$$

Subtract 12 from 1 to get -11.

$$5a^{2}+2a-11+32a-8a^{2}+3a^{2}-a$$

Combine 2a and 32a to get 34a.

$$5a^{2}+34a-11-8a^{2}+3a^{2}-a$$

Combine 5a^{2} and -8a^{2} to get -3a^{2}.

$$-3a^{2}+34a-11+3a^{2}-a$$

Combine -3a^{2} and 3a^{2} to get 0.

$$34a-11-a$$

Combine 34a and -a to get 33a.

$$33a-11$$

Expand

$$33a-11$$

Solution Steps

Use the distributive property to multiply -4 by 3-8a+2a^{2}.

$$5a^{2}+2a+1-12+32a-8a^{2}+3a^{2}-a$$

Subtract 12 from 1 to get -11.

$$5a^{2}+2a-11+32a-8a^{2}+3a^{2}-a$$

Combine 2a and 32a to get 34a.

$$5a^{2}+34a-11-8a^{2}+3a^{2}-a$$

Combine 5a^{2} and -8a^{2} to get -3a^{2}.

$$-3a^{2}+34a-11+3a^{2}-a$$

Combine -3a^{2} and 3a^{2} to get 0.

$$34a-11-a$$

Combine 34a and -a to get 33a.

$$33a-11$$