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

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

Evaluate

$$x\left(x-1\right)\left(x^{2}-4\right)$$

Solution Steps

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

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

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

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

Combine 2x^{2} and -2x^{2} to get 0.

$$\left(x^{3}-4x\right)\left(x-1\right)$$

Apply the distributive property by multiplying each term of x^{3}-4x by each term of x-1.

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

Expand

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

Solution Steps

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

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

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

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

Combine 2x^{2} and -2x^{2} to get 0.

$$\left(x^{3}-4x\right)\left(x-1\right)$$

Apply the distributive property by multiplying each term of x^{3}-4x by each term of x-1.

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