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

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

Evaluate

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

Solution Steps

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

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

Combine x and 2x to get 3x.

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

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

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

Apply the distributive property by multiplying each term of x^{3}+3x^{2}+2x by each term of x-1.

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

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

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

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

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

Expand

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

Solution Steps

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

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

Combine x and 2x to get 3x.

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

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

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

Apply the distributive property by multiplying each term of x^{3}+3x^{2}+2x by each term of x-1.

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

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

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

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

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