Solve 2(z+3)(z+2)(z+1)

$$2 ( z + 3 ) ( z + 2 ) ( z + 1 )$$

Evaluate

$$2\left(z+1\right)\left(z+2\right)\left(z+3\right)$$

Solution Steps

Use the distributive property to multiply 2 by z+3.

$$\left(2z+6\right)\left(z+2\right)\left(z+1\right)$$

Apply the distributive property by multiplying each term of 2z+6 by each term of z+2.

$$\left(2z^{2}+4z+6z+12\right)\left(z+1\right)$$

Combine 4z and 6z to get 10z.

$$\left(2z^{2}+10z+12\right)\left(z+1\right)$$

Apply the distributive property by multiplying each term of 2z^{2}+10z+12 by each term of z+1.

$$2z^{3}+2z^{2}+10z^{2}+10z+12z+12$$

Combine 2z^{2} and 10z^{2} to get 12z^{2}.

$$2z^{3}+12z^{2}+10z+12z+12$$

Combine 10z and 12z to get 22z.

$$2z^{3}+12z^{2}+22z+12$$

Expand

$$2z^{3}+12z^{2}+22z+12$$

Solution Steps

Use the distributive property to multiply 2 by z+3.

$$\left(2z+6\right)\left(z+2\right)\left(z+1\right)$$

Apply the distributive property by multiplying each term of 2z+6 by each term of z+2.

$$\left(2z^{2}+4z+6z+12\right)\left(z+1\right)$$

Combine 4z and 6z to get 10z.

$$\left(2z^{2}+10z+12\right)\left(z+1\right)$$

Apply the distributive property by multiplying each term of 2z^{2}+10z+12 by each term of z+1.

$$2z^{3}+2z^{2}+10z^{2}+10z+12z+12$$

Combine 2z^{2} and 10z^{2} to get 12z^{2}.

$$2z^{3}+12z^{2}+10z+12z+12$$

Combine 10z and 12z to get 22z.

$$2z^{3}+12z^{2}+22z+12$$