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

$$x ( x + 1 ) ( x + 2 ) + ( x - 1 ) ( x - 2 )$$

Evaluate

$$x^{3}+4x^{2}-x+2$$

Solution Steps

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

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

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

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

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

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

Apply the distributive property by multiplying each term of x-1 by each term of x-2.

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

Combine -2x and -x to get -3x.

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

Combine 3x^{2} and x^{2} to get 4x^{2}.

$$x^{3}+4x^{2}+2x-3x+2$$

Combine 2x and -3x to get -x.

$$x^{3}+4x^{2}-x+2$$

Expand

$$x^{3}+4x^{2}-x+2$$

Solution Steps

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

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

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

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

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

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

Apply the distributive property by multiplying each term of x-1 by each term of x-2.

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

Combine -2x and -x to get -3x.

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

Combine 3x^{2} and x^{2} to get 4x^{2}.

$$x^{3}+4x^{2}+2x-3x+2$$

Combine 2x and -3x to get -x.

$$x^{3}+4x^{2}-x+2$$