Solve (x+1)(x+2)(x-3)(x-4)-84

$$( x + 1 ) ( x + 2 ) ( x - 3 ) ( x - 4 ) - 84$$

Evaluate

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

Solution Steps

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

$$\left(x^{2}+2x+x+2\right)\left(x-3\right)\left(x-4\right)-84$$

Combine 2x and x to get 3x.

$$\left(x^{2}+3x+2\right)\left(x-3\right)\left(x-4\right)-84$$

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

$$\left(x^{3}-3x^{2}+3x^{2}-9x+2x-6\right)\left(x-4\right)-84$$

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

$$\left(x^{3}-9x+2x-6\right)\left(x-4\right)-84$$

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

$$\left(x^{3}-7x-6\right)\left(x-4\right)-84$$

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

$$x^{4}-4x^{3}-7x^{2}+28x-6x+24-84$$

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

$$x^{4}-4x^{3}-7x^{2}+22x+24-84$$

Subtract 84 from 24 to get -60.

$$x^{4}-4x^{3}-7x^{2}+22x-60$$

Expand

$$x^{4}-4x^{3}-7x^{2}+22x-60$$

Solution Steps

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

$$\left(x^{2}+2x+x+2\right)\left(x-3\right)\left(x-4\right)-84$$

Combine 2x and x to get 3x.

$$\left(x^{2}+3x+2\right)\left(x-3\right)\left(x-4\right)-84$$

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

$$\left(x^{3}-3x^{2}+3x^{2}-9x+2x-6\right)\left(x-4\right)-84$$

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

$$\left(x^{3}-9x+2x-6\right)\left(x-4\right)-84$$

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

$$\left(x^{3}-7x-6\right)\left(x-4\right)-84$$

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

$$x^{4}-4x^{3}-7x^{2}+28x-6x+24-84$$

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

$$x^{4}-4x^{3}-7x^{2}+22x+24-84$$

Subtract 84 from 24 to get -60.

$$x^{4}-4x^{3}-7x^{2}+22x-60$$