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

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

Evaluate

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

Solution Steps

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

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

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

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

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

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

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

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

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

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

Combine x^{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

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

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

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

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

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

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

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

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

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

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

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

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