Solve 1*left(x-1right)left(x+2right)left(x-2right)left(x-3right)

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

Evaluate

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

Solution Steps

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

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

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

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

Combine 2x and -x to get x.

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

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

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

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

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

Combine -2x and -2x to get -4x.

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

Apply the distributive property by multiplying each term of x^{3}-x^{2}-4x+4 by each term of x-3.

$$x^{4}-3x^{3}-x^{3}+3x^{2}-4x^{2}+12x+4x-12$$

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

$$x^{4}-4x^{3}+3x^{2}-4x^{2}+12x+4x-12$$

Combine 3x^{2} and -4x^{2} to get -x^{2}.

$$x^{4}-4x^{3}-x^{2}+12x+4x-12$$

Combine 12x and 4x to get 16x.

$$x^{4}-4x^{3}-x^{2}+16x-12$$

Expand

$$x^{4}-4x^{3}-x^{2}+16x-12$$

Solution Steps

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

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

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

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

Combine 2x and -x to get x.

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

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

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

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

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

Combine -2x and -2x to get -4x.

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

Apply the distributive property by multiplying each term of x^{3}-x^{2}-4x+4 by each term of x-3.

$$x^{4}-3x^{3}-x^{3}+3x^{2}-4x^{2}+12x+4x-12$$

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

$$x^{4}-4x^{3}+3x^{2}-4x^{2}+12x+4x-12$$

Combine 3x^{2} and -4x^{2} to get -x^{2}.

$$x^{4}-4x^{3}-x^{2}+12x+4x-12$$

Combine 12x and 4x to get 16x.

$$x^{4}-4x^{3}-x^{2}+16x-12$$