Solve x*(x-1)*(x-2)*(x-3)=

$$x \times (x-1) \times (x-2) \times (x-3)=$$

Evaluate

$$x\left(x-3\right)\left(x-2\right)\left(x-1\right)$$

Solution Steps

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

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

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

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

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

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

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

$$x^{4}-3x^{3}-3x^{3}+9x^{2}+2x^{2}-6x$$

Combine -3x^{3} and -3x^{3} to get -6x^{3}.

$$x^{4}-6x^{3}+9x^{2}+2x^{2}-6x$$

Combine 9x^{2} and 2x^{2} to get 11x^{2}.

$$x^{4}-6x^{3}+11x^{2}-6x$$

Expand

$$x^{4}-6x^{3}+11x^{2}-6x$$

Solution Steps

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

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

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

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

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

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

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

$$x^{4}-3x^{3}-3x^{3}+9x^{2}+2x^{2}-6x$$

Combine -3x^{3} and -3x^{3} to get -6x^{3}.

$$x^{4}-6x^{3}+9x^{2}+2x^{2}-6x$$

Combine 9x^{2} and 2x^{2} to get 11x^{2}.

$$x^{4}-6x^{3}+11x^{2}-6x$$