Solve (s+t)(s+1)+(s+1)(s+1)+2(s+1)(s+1)

$$( s + t ) ( s + 1 ) + ( s + 1 ) ( s + 1 ) + 2 ( s + 1 ) ( s + 1 )$$

Evaluate

$$\left(s+1\right)\left(4s+t+3\right)$$

Solution Steps

Multiply s+1 and s+1 to get \left(s+1\right)^{2}.

$$\left(s+t\right)\left(s+1\right)+\left(s+1\right)^{2}+2\left(s+1\right)\left(s+1\right)$$

Multiply s+1 and s+1 to get \left(s+1\right)^{2}.

$$\left(s+t\right)\left(s+1\right)+\left(s+1\right)^{2}+2\left(s+1\right)^{2}$$

Apply the distributive property by multiplying each term of s+t by each term of s+1.

$$s^{2}+s+ts+t+\left(s+1\right)^{2}+2\left(s+1\right)^{2}$$

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(s+1\right)^{2}.

$$s^{2}+s+ts+t+s^{2}+2s+1+2\left(s+1\right)^{2}$$

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

$$2s^{2}+s+ts+t+2s+1+2\left(s+1\right)^{2}$$

Combine s and 2s to get 3s.

$$2s^{2}+3s+ts+t+1+2\left(s+1\right)^{2}$$

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(s+1\right)^{2}.

$$2s^{2}+3s+ts+t+1+2\left(s^{2}+2s+1\right)$$

Use the distributive property to multiply 2 by s^{2}+2s+1.

$$2s^{2}+3s+ts+t+1+2s^{2}+4s+2$$

Combine 2s^{2} and 2s^{2} to get 4s^{2}.

$$4s^{2}+3s+ts+t+1+4s+2$$

Combine 3s and 4s to get 7s.

$$4s^{2}+7s+ts+t+1+2$$

Add 1 and 2 to get 3.

$$4s^{2}+7s+ts+t+3$$

Expand

$$4s^{2}+st+7s+t+3$$

Solution Steps

Multiply s+1 and s+1 to get \left(s+1\right)^{2}.

$$\left(s+t\right)\left(s+1\right)+\left(s+1\right)^{2}+2\left(s+1\right)\left(s+1\right)$$

Multiply s+1 and s+1 to get \left(s+1\right)^{2}.

$$\left(s+t\right)\left(s+1\right)+\left(s+1\right)^{2}+2\left(s+1\right)^{2}$$

Apply the distributive property by multiplying each term of s+t by each term of s+1.

$$s^{2}+s+ts+t+\left(s+1\right)^{2}+2\left(s+1\right)^{2}$$

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(s+1\right)^{2}.

$$s^{2}+s+ts+t+s^{2}+2s+1+2\left(s+1\right)^{2}$$

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

$$2s^{2}+s+ts+t+2s+1+2\left(s+1\right)^{2}$$

Combine s and 2s to get 3s.

$$2s^{2}+3s+ts+t+1+2\left(s+1\right)^{2}$$

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(s+1\right)^{2}.

$$2s^{2}+3s+ts+t+1+2\left(s^{2}+2s+1\right)$$

Use the distributive property to multiply 2 by s^{2}+2s+1.

$$2s^{2}+3s+ts+t+1+2s^{2}+4s+2$$

Combine 2s^{2} and 2s^{2} to get 4s^{2}.

$$4s^{2}+3s+ts+t+1+4s+2$$

Combine 3s and 4s to get 7s.

$$4s^{2}+7s+ts+t+1+2$$

Add 1 and 2 to get 3.

$$4s^{2}+7s+ts+t+3$$