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

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

Evaluate

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

Solution Steps

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

$$\left(x^{2}-3x+2x-6\right)\left(x+1\right)\left(x-1\right)$$

Combine -3x and 2x to get -x.

$$\left(x^{2}-x-6\right)\left(x+1\right)\left(x-1\right)$$

Apply the distributive property by multiplying each term of x^{2}-x-6 by each term of x+1.

$$\left(x^{3}+x^{2}-x^{2}-x-6x-6\right)\left(x-1\right)$$

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

$$\left(x^{3}-x-6x-6\right)\left(x-1\right)$$

Combine -x and -6x to get -7x.

$$\left(x^{3}-7x-6\right)\left(x-1\right)$$

Apply the distributive property by multiplying each term of x^{3}-7x-6 by each term of x-1.

$$x^{4}-x^{3}-7x^{2}+7x-6x+6$$

Combine 7x and -6x to get x.

$$x^{4}-x^{3}-7x^{2}+x+6$$

Expand

$$x^{4}-x^{3}-7x^{2}+x+6$$

Solution Steps

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

$$\left(x^{2}-3x+2x-6\right)\left(x+1\right)\left(x-1\right)$$

Combine -3x and 2x to get -x.

$$\left(x^{2}-x-6\right)\left(x+1\right)\left(x-1\right)$$

Apply the distributive property by multiplying each term of x^{2}-x-6 by each term of x+1.

$$\left(x^{3}+x^{2}-x^{2}-x-6x-6\right)\left(x-1\right)$$

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

$$\left(x^{3}-x-6x-6\right)\left(x-1\right)$$

Combine -x and -6x to get -7x.

$$\left(x^{3}-7x-6\right)\left(x-1\right)$$

Apply the distributive property by multiplying each term of x^{3}-7x-6 by each term of x-1.

$$x^{4}-x^{3}-7x^{2}+7x-6x+6$$

Combine 7x and -6x to get x.

$$x^{4}-x^{3}-7x^{2}+x+6$$