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

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

Evaluate

$$\left(x-1\right)\left(x+2\right)\left(x^{2}-9\right)$$

Solution Steps

Apply the distributive property by multiplying each term of x-1 by each term of x+3.

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

Combine 3x and -x to get 2x.

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

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

$$\left(x^{3}+2x^{2}+2x^{2}+4x-3x-6\right)\left(x-3\right)$$

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

$$\left(x^{3}+4x^{2}+4x-3x-6\right)\left(x-3\right)$$

Combine 4x and -3x to get x.

$$\left(x^{3}+4x^{2}+x-6\right)\left(x-3\right)$$

Apply the distributive property by multiplying each term of x^{3}+4x^{2}+x-6 by each term of x-3.

$$x^{4}-3x^{3}+4x^{3}-12x^{2}+x^{2}-3x-6x+18$$

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

$$x^{4}+x^{3}-12x^{2}+x^{2}-3x-6x+18$$

Combine -12x^{2} and x^{2} to get -11x^{2}.

$$x^{4}+x^{3}-11x^{2}-3x-6x+18$$

Combine -3x and -6x to get -9x.

$$x^{4}+x^{3}-11x^{2}-9x+18$$

Expand

$$x^{4}+x^{3}-11x^{2}-9x+18$$

Solution Steps

Apply the distributive property by multiplying each term of x-1 by each term of x+3.

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

Combine 3x and -x to get 2x.

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

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

$$\left(x^{3}+2x^{2}+2x^{2}+4x-3x-6\right)\left(x-3\right)$$

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

$$\left(x^{3}+4x^{2}+4x-3x-6\right)\left(x-3\right)$$

Combine 4x and -3x to get x.

$$\left(x^{3}+4x^{2}+x-6\right)\left(x-3\right)$$

Apply the distributive property by multiplying each term of x^{3}+4x^{2}+x-6 by each term of x-3.

$$x^{4}-3x^{3}+4x^{3}-12x^{2}+x^{2}-3x-6x+18$$

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

$$x^{4}+x^{3}-12x^{2}+x^{2}-3x-6x+18$$

Combine -12x^{2} and x^{2} to get -11x^{2}.

$$x^{4}+x^{3}-11x^{2}-3x-6x+18$$

Combine -3x and -6x to get -9x.

$$x^{4}+x^{3}-11x^{2}-9x+18$$