Solve s(s+1)(s+2)(s+4)

$$s ( s + 1 ) ( s + 2 ) ( s + 4 )$$

Expand

$$s^{4}+7s^{3}+14s^{2}+8s$$

Solution Steps

Use the distributive property to multiply s by s+1.

$$\left(s^{2}+s\right)\left(s+2\right)\left(s+4\right)$$

Apply the distributive property by multiplying each term of s^{2}+s by each term of s+2.

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

Combine 2s^{2} and s^{2} to get 3s^{2}.

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

Apply the distributive property by multiplying each term of s^{3}+3s^{2}+2s by each term of s+4.

$$s^{4}+4s^{3}+3s^{3}+12s^{2}+2s^{2}+8s$$

Combine 4s^{3} and 3s^{3} to get 7s^{3}.

$$s^{4}+7s^{3}+12s^{2}+2s^{2}+8s$$

Combine 12s^{2} and 2s^{2} to get 14s^{2}.

$$s^{4}+7s^{3}+14s^{2}+8s$$

Evaluate

$$s\left(s+1\right)\left(s+2\right)\left(s+4\right)$$

Solution Steps

Use the distributive property to multiply s by s+1.

$$\left(s^{2}+s\right)\left(s+2\right)\left(s+4\right)$$

Apply the distributive property by multiplying each term of s^{2}+s by each term of s+2.

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

Combine 2s^{2} and s^{2} to get 3s^{2}.

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

Apply the distributive property by multiplying each term of s^{3}+3s^{2}+2s by each term of s+4.

$$s^{4}+4s^{3}+3s^{3}+12s^{2}+2s^{2}+8s$$

Combine 4s^{3} and 3s^{3} to get 7s^{3}.

$$s^{4}+7s^{3}+12s^{2}+2s^{2}+8s$$

Combine 12s^{2} and 2s^{2} to get 14s^{2}.

$$s^{4}+7s^{3}+14s^{2}+8s$$