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

$$2 ( - 3 a ( a - 1 ) - ( a + 1 ) ( a + 2 )$$

Evaluate

$$-8a^{2}-4$$

Solution Steps

Use the distributive property to multiply -3a by a-1.

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

Apply the distributive property by multiplying each term of a+1 by each term of a+2.

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

Combine 2a and a to get 3a.

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

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

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

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

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

Combine 3a and -3a to get 0.

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

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

$$-8a^{2}-4$$

Expand

$$-8a^{2}-4$$

Solution Steps

Use the distributive property to multiply -3a by a-1.

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

Apply the distributive property by multiplying each term of a+1 by each term of a+2.

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

Combine 2a and a to get 3a.

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

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

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

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

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

Combine 3a and -3a to get 0.

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

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

$$-8a^{2}-4$$