Solve (x-1)(x-2)(x+3)(x+4)-6

$$( x - 1 ) ( x - 2 ) ( x + 3 ) ( x + 4 ) - 6$$

Evaluate

$$\left(x-2\right)\left(x-1\right)\left(x+3\right)\left(x+4\right)-6$$

Solution Steps

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

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

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

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

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

$$\left(x^{3}+3x^{2}-3x^{2}-9x+2x+6\right)\left(x+4\right)-6$$

Combine 3x^{2} and -3x^{2} to get 0.

$$\left(x^{3}-9x+2x+6\right)\left(x+4\right)-6$$

Combine -9x and 2x to get -7x.

$$\left(x^{3}-7x+6\right)\left(x+4\right)-6$$

Apply the distributive property by multiplying each term of x^{3}-7x+6 by each term of x+4.

$$x^{4}+4x^{3}-7x^{2}-28x+6x+24-6$$

Combine -28x and 6x to get -22x.

$$x^{4}+4x^{3}-7x^{2}-22x+24-6$$

Subtract 6 from 24 to get 18.

$$x^{4}+4x^{3}-7x^{2}-22x+18$$

Expand

$$x^{4}+4x^{3}-7x^{2}-22x+18$$

Solution Steps

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

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

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

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

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

$$\left(x^{3}+3x^{2}-3x^{2}-9x+2x+6\right)\left(x+4\right)-6$$

Combine 3x^{2} and -3x^{2} to get 0.

$$\left(x^{3}-9x+2x+6\right)\left(x+4\right)-6$$

Combine -9x and 2x to get -7x.

$$\left(x^{3}-7x+6\right)\left(x+4\right)-6$$

Apply the distributive property by multiplying each term of x^{3}-7x+6 by each term of x+4.

$$x^{4}+4x^{3}-7x^{2}-28x+6x+24-6$$

Combine -28x and 6x to get -22x.

$$x^{4}+4x^{3}-7x^{2}-22x+24-6$$

Subtract 6 from 24 to get 18.

$$x^{4}+4x^{3}-7x^{2}-22x+18$$