Solve left(3a-4right)left(4a^2+9a+2right)+(3a+6)left(4a+1right)

$$\left( 3a-4 \right) \left( 4 { a }^{ 2 } +9a+2 \right) +(3a+6) \left( 4a+1 \right)$$

Evaluate

$$\left(3a-1\right)\left(a+2\right)\left(4a+1\right)$$

Solution Steps

Use the distributive property to multiply 3a-4 by 4a^{2}+9a+2 and combine like terms.

$$12a^{3}+11a^{2}-30a-8+\left(3a+6\right)\left(4a+1\right)$$

Use the distributive property to multiply 3a+6 by 4a+1 and combine like terms.

$$12a^{3}+11a^{2}-30a-8+12a^{2}+27a+6$$

Combine 11a^{2} and 12a^{2} to get 23a^{2}.

$$12a^{3}+23a^{2}-30a-8+27a+6$$

Combine -30a and 27a to get -3a.

$$12a^{3}+23a^{2}-3a-8+6$$

Add -8 and 6 to get -2.

$$12a^{3}+23a^{2}-3a-2$$

Expand

$$12a^{3}+23a^{2}-3a-2$$

Solution Steps

Use the distributive property to multiply 3a-4 by 4a^{2}+9a+2 and combine like terms.

$$12a^{3}+11a^{2}-30a-8+\left(3a+6\right)\left(4a+1\right)$$

Use the distributive property to multiply 3a+6 by 4a+1 and combine like terms.

$$12a^{3}+11a^{2}-30a-8+12a^{2}+27a+6$$

Combine 11a^{2} and 12a^{2} to get 23a^{2}.

$$12a^{3}+23a^{2}-30a-8+27a+6$$

Combine -30a and 27a to get -3a.

$$12a^{3}+23a^{2}-3a-8+6$$

Add -8 and 6 to get -2.

$$12a^{3}+23a^{2}-3a-2$$