Solve (x+1)(2x^2+1)+(x+1)(-x+2)+(x^2+3)(x+2)

$$(x+1)(2 { x }^{ 2 } +1)+(x+1)(-x+2)+( { x }^{ 2 } +3)(x+2)$$

Evaluate

$$3x^{3}+3x^{2}+5x+9$$

Solution Steps

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

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

Use the distributive property to multiply x+1 by -x+2.

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

Combine x and 2x to get 3x.

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

Add 1 and 2 to get 3.

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

Use the distributive property to multiply x^{2}+3 by x+2.

$$2x^{3}+3x+2x^{2}+3+x\left(-x\right)-x+x^{3}+2x^{2}+3x+6$$

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

$$3x^{3}+3x+2x^{2}+3+x\left(-x\right)-x+2x^{2}+3x+6$$

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

$$3x^{3}+3x+4x^{2}+3+x\left(-x\right)-x+3x+6$$

Combine 3x and 3x to get 6x.

$$3x^{3}+6x+4x^{2}+3+x\left(-x\right)-x+6$$

Add 3 and 6 to get 9.

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

Multiply x and x to get x^{2}.

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

Combine 4x^{2} and x^{2}\left(-1\right) to get 3x^{2}.

$$3x^{3}+6x+3x^{2}+9-x$$

Combine 6x and -x to get 5x.

$$3x^{3}+5x+3x^{2}+9$$

Expand

$$3x^{3}+3x^{2}+5x+9$$

Solution Steps

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

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

Use the distributive property to multiply x+1 by -x+2.

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

Combine x and 2x to get 3x.

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

Add 1 and 2 to get 3.

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

Use the distributive property to multiply x^{2}+3 by x+2.

$$2x^{3}+3x+2x^{2}+3+x\left(-x\right)-x+x^{3}+2x^{2}+3x+6$$

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

$$3x^{3}+3x+2x^{2}+3+x\left(-x\right)-x+2x^{2}+3x+6$$

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

$$3x^{3}+3x+4x^{2}+3+x\left(-x\right)-x+3x+6$$

Combine 3x and 3x to get 6x.

$$3x^{3}+6x+4x^{2}+3+x\left(-x\right)-x+6$$

Add 3 and 6 to get 9.

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

Multiply x and x to get x^{2}.

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

Combine 4x^{2} and x^{2}\left(-1\right) to get 3x^{2}.

$$3x^{3}+6x+3x^{2}+9-x$$

Combine 6x and -x to get 5x.

$$3x^{3}+5x+3x^{2}+9$$