Solve (x+1)(x-2)(x+3)(x-4)

$$(x+1)(x-2)(x+3)(x-4)$$

Evaluate

$$\left(x-4\right)\left(x-2\right)\left(x+1\right)\left(x+3\right)$$

Solution Steps

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

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

Combine -2x and x to get -x.

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

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

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

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

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

Combine -3x and -2x to get -5x.

$$\left(x^{3}+2x^{2}-5x-6\right)\left(x-4\right)$$

Apply the distributive property by multiplying each term of x^{3}+2x^{2}-5x-6 by each term of x-4.

$$x^{4}-4x^{3}+2x^{3}-8x^{2}-5x^{2}+20x-6x+24$$

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

$$x^{4}-2x^{3}-8x^{2}-5x^{2}+20x-6x+24$$

Combine -8x^{2} and -5x^{2} to get -13x^{2}.

$$x^{4}-2x^{3}-13x^{2}+20x-6x+24$$

Combine 20x and -6x to get 14x.

$$x^{4}-2x^{3}-13x^{2}+14x+24$$

Expand

$$x^{4}-2x^{3}-13x^{2}+14x+24$$

Solution Steps

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

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

Combine -2x and x to get -x.

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

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

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

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

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

Combine -3x and -2x to get -5x.

$$\left(x^{3}+2x^{2}-5x-6\right)\left(x-4\right)$$

Apply the distributive property by multiplying each term of x^{3}+2x^{2}-5x-6 by each term of x-4.

$$x^{4}-4x^{3}+2x^{3}-8x^{2}-5x^{2}+20x-6x+24$$

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

$$x^{4}-2x^{3}-8x^{2}-5x^{2}+20x-6x+24$$

Combine -8x^{2} and -5x^{2} to get -13x^{2}.

$$x^{4}-2x^{3}-13x^{2}+20x-6x+24$$

Combine 20x and -6x to get 14x.

$$x^{4}-2x^{3}-13x^{2}+14x+24$$