Solve (x-1)(x-2)(x-3)(x-4)-24

$$( x - 1 ) ( x - 2 ) ( x - 3 ) ( x - 4 ) - 24$$

Evaluate

$$x\left(x-5\right)\left(x^{2}-5x+10\right)$$

Solution Steps

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

$$\left(x^{2}-2x-x+2\right)\left(x-3\right)\left(x-4\right)-24$$

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

$$\left(x^{2}-3x+2\right)\left(x-3\right)\left(x-4\right)-24$$

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

$$\left(x^{3}-3x^{2}-3x^{2}+9x+2x-6\right)\left(x-4\right)-24$$

Combine -3x^{2} and -3x^{2} to get -6x^{2}.

$$\left(x^{3}-6x^{2}+9x+2x-6\right)\left(x-4\right)-24$$

Combine 9x and 2x to get 11x.

$$\left(x^{3}-6x^{2}+11x-6\right)\left(x-4\right)-24$$

Apply the distributive property by multiplying each term of x^{3}-6x^{2}+11x-6 by each term of x-4.

$$x^{4}-4x^{3}-6x^{3}+24x^{2}+11x^{2}-44x-6x+24-24$$

Combine -4x^{3} and -6x^{3} to get -10x^{3}.

$$x^{4}-10x^{3}+24x^{2}+11x^{2}-44x-6x+24-24$$

Combine 24x^{2} and 11x^{2} to get 35x^{2}.

$$x^{4}-10x^{3}+35x^{2}-44x-6x+24-24$$

Combine -44x and -6x to get -50x.

$$x^{4}-10x^{3}+35x^{2}-50x+24-24$$

Subtract 24 from 24 to get 0.

$$x^{4}-10x^{3}+35x^{2}-50x$$

Expand

$$x^{4}-10x^{3}+35x^{2}-50x$$

Solution Steps

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

$$\left(x^{2}-2x-x+2\right)\left(x-3\right)\left(x-4\right)-24$$

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

$$\left(x^{2}-3x+2\right)\left(x-3\right)\left(x-4\right)-24$$

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

$$\left(x^{3}-3x^{2}-3x^{2}+9x+2x-6\right)\left(x-4\right)-24$$

Combine -3x^{2} and -3x^{2} to get -6x^{2}.

$$\left(x^{3}-6x^{2}+9x+2x-6\right)\left(x-4\right)-24$$

Combine 9x and 2x to get 11x.

$$\left(x^{3}-6x^{2}+11x-6\right)\left(x-4\right)-24$$

Apply the distributive property by multiplying each term of x^{3}-6x^{2}+11x-6 by each term of x-4.

$$x^{4}-4x^{3}-6x^{3}+24x^{2}+11x^{2}-44x-6x+24-24$$

Combine -4x^{3} and -6x^{3} to get -10x^{3}.

$$x^{4}-10x^{3}+24x^{2}+11x^{2}-44x-6x+24-24$$

Combine 24x^{2} and 11x^{2} to get 35x^{2}.

$$x^{4}-10x^{3}+35x^{2}-44x-6x+24-24$$

Combine -44x and -6x to get -50x.

$$x^{4}-10x^{3}+35x^{2}-50x+24-24$$

Subtract 24 from 24 to get 0.

$$x^{4}-10x^{3}+35x^{2}-50x$$