Solve x(x+1)(x-2)(x-3)

$$x(x+1)(x-2)(x-3)$$

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 -x^{2}.

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

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

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

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

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

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

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

Expand

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

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 -x^{2}.

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

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

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

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

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

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

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