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

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

Evaluate

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

Solution Steps

Apply the distributive property by multiplying each term of x-4 by each term of x-3.

$$\left(x^{2}-3x-4x+12\right)\left(x-2\right)\left(x-1\right)x$$

Combine -3x and -4x to get -7x.

$$\left(x^{2}-7x+12\right)\left(x-2\right)\left(x-1\right)x$$

Apply the distributive property by multiplying each term of x^{2}-7x+12 by each term of x-2.

$$\left(x^{3}-2x^{2}-7x^{2}+14x+12x-24\right)\left(x-1\right)x$$

Combine -2x^{2} and -7x^{2} to get -9x^{2}.

$$\left(x^{3}-9x^{2}+14x+12x-24\right)\left(x-1\right)x$$

Combine 14x and 12x to get 26x.

$$\left(x^{3}-9x^{2}+26x-24\right)\left(x-1\right)x$$

Apply the distributive property by multiplying each term of x^{3}-9x^{2}+26x-24 by each term of x-1.

$$\left(x^{4}-x^{3}-9x^{3}+9x^{2}+26x^{2}-26x-24x+24\right)x$$

Combine -x^{3} and -9x^{3} to get -10x^{3}.

$$\left(x^{4}-10x^{3}+9x^{2}+26x^{2}-26x-24x+24\right)x$$

Combine 9x^{2} and 26x^{2} to get 35x^{2}.

$$\left(x^{4}-10x^{3}+35x^{2}-26x-24x+24\right)x$$

Combine -26x and -24x to get -50x.

$$\left(x^{4}-10x^{3}+35x^{2}-50x+24\right)x$$

Use the distributive property to multiply x^{4}-10x^{3}+35x^{2}-50x+24 by x.

$$x^{5}-10x^{4}+35x^{3}-50x^{2}+24x$$

Expand

$$x^{5}-10x^{4}+35x^{3}-50x^{2}+24x$$

Solution Steps

Apply the distributive property by multiplying each term of x-4 by each term of x-3.

$$\left(x^{2}-3x-4x+12\right)\left(x-2\right)\left(x-1\right)x$$

Combine -3x and -4x to get -7x.

$$\left(x^{2}-7x+12\right)\left(x-2\right)\left(x-1\right)x$$

Apply the distributive property by multiplying each term of x^{2}-7x+12 by each term of x-2.

$$\left(x^{3}-2x^{2}-7x^{2}+14x+12x-24\right)\left(x-1\right)x$$

Combine -2x^{2} and -7x^{2} to get -9x^{2}.

$$\left(x^{3}-9x^{2}+14x+12x-24\right)\left(x-1\right)x$$

Combine 14x and 12x to get 26x.

$$\left(x^{3}-9x^{2}+26x-24\right)\left(x-1\right)x$$

Apply the distributive property by multiplying each term of x^{3}-9x^{2}+26x-24 by each term of x-1.

$$\left(x^{4}-x^{3}-9x^{3}+9x^{2}+26x^{2}-26x-24x+24\right)x$$

Combine -x^{3} and -9x^{3} to get -10x^{3}.

$$\left(x^{4}-10x^{3}+9x^{2}+26x^{2}-26x-24x+24\right)x$$

Combine 9x^{2} and 26x^{2} to get 35x^{2}.

$$\left(x^{4}-10x^{3}+35x^{2}-26x-24x+24\right)x$$

Combine -26x and -24x to get -50x.

$$\left(x^{4}-10x^{3}+35x^{2}-50x+24\right)x$$

Use the distributive property to multiply x^{4}-10x^{3}+35x^{2}-50x+24 by x.

$$x^{5}-10x^{4}+35x^{3}-50x^{2}+24x$$