Solve x(x-1)(x-2)(x-3)(x-4)(x-5)

$$x(x-1)(x-2)(x-3)(x-4)(x-5)$$

Evaluate

$$x\left(x-5\right)\left(x-4\right)\left(x-3\right)\left(x-2\right)\left(x-1\right)$$

Solution Steps

Use the distributive property to multiply x by x-1.

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

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

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

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

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

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

$$\left(x^{4}-3x^{3}-3x^{3}+9x^{2}+2x^{2}-6x\right)\left(x-4\right)\left(x-5\right)$$

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

$$\left(x^{4}-6x^{3}+9x^{2}+2x^{2}-6x\right)\left(x-4\right)\left(x-5\right)$$

Combine 9x^{2} and 2x^{2} to get 11x^{2}.

$$\left(x^{4}-6x^{3}+11x^{2}-6x\right)\left(x-4\right)\left(x-5\right)$$

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

$$\left(x^{5}-4x^{4}-6x^{4}+24x^{3}+11x^{3}-44x^{2}-6x^{2}+24x\right)\left(x-5\right)$$

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

$$\left(x^{5}-10x^{4}+24x^{3}+11x^{3}-44x^{2}-6x^{2}+24x\right)\left(x-5\right)$$

Combine 24x^{3} and 11x^{3} to get 35x^{3}.

$$\left(x^{5}-10x^{4}+35x^{3}-44x^{2}-6x^{2}+24x\right)\left(x-5\right)$$

Combine -44x^{2} and -6x^{2} to get -50x^{2}.

$$\left(x^{5}-10x^{4}+35x^{3}-50x^{2}+24x\right)\left(x-5\right)$$

Apply the distributive property by multiplying each term of x^{5}-10x^{4}+35x^{3}-50x^{2}+24x by each term of x-5.

$$x^{6}-5x^{5}-10x^{5}+50x^{4}+35x^{4}-175x^{3}-50x^{3}+250x^{2}+24x^{2}-120x$$

Combine -5x^{5} and -10x^{5} to get -15x^{5}.

$$x^{6}-15x^{5}+50x^{4}+35x^{4}-175x^{3}-50x^{3}+250x^{2}+24x^{2}-120x$$

Combine 50x^{4} and 35x^{4} to get 85x^{4}.

$$x^{6}-15x^{5}+85x^{4}-175x^{3}-50x^{3}+250x^{2}+24x^{2}-120x$$

Combine -175x^{3} and -50x^{3} to get -225x^{3}.

$$x^{6}-15x^{5}+85x^{4}-225x^{3}+250x^{2}+24x^{2}-120x$$

Combine 250x^{2} and 24x^{2} to get 274x^{2}.

$$x^{6}-15x^{5}+85x^{4}-225x^{3}+274x^{2}-120x$$

Expand

$$x^{6}-15x^{5}+85x^{4}-225x^{3}+274x^{2}-120x$$

Solution Steps

Use the distributive property to multiply x by x-1.

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

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

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

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

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

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

$$\left(x^{4}-3x^{3}-3x^{3}+9x^{2}+2x^{2}-6x\right)\left(x-4\right)\left(x-5\right)$$

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

$$\left(x^{4}-6x^{3}+9x^{2}+2x^{2}-6x\right)\left(x-4\right)\left(x-5\right)$$

Combine 9x^{2} and 2x^{2} to get 11x^{2}.

$$\left(x^{4}-6x^{3}+11x^{2}-6x\right)\left(x-4\right)\left(x-5\right)$$

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

$$\left(x^{5}-4x^{4}-6x^{4}+24x^{3}+11x^{3}-44x^{2}-6x^{2}+24x\right)\left(x-5\right)$$

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

$$\left(x^{5}-10x^{4}+24x^{3}+11x^{3}-44x^{2}-6x^{2}+24x\right)\left(x-5\right)$$

Combine 24x^{3} and 11x^{3} to get 35x^{3}.

$$\left(x^{5}-10x^{4}+35x^{3}-44x^{2}-6x^{2}+24x\right)\left(x-5\right)$$

Combine -44x^{2} and -6x^{2} to get -50x^{2}.

$$\left(x^{5}-10x^{4}+35x^{3}-50x^{2}+24x\right)\left(x-5\right)$$

Apply the distributive property by multiplying each term of x^{5}-10x^{4}+35x^{3}-50x^{2}+24x by each term of x-5.

$$x^{6}-5x^{5}-10x^{5}+50x^{4}+35x^{4}-175x^{3}-50x^{3}+250x^{2}+24x^{2}-120x$$

Combine -5x^{5} and -10x^{5} to get -15x^{5}.

$$x^{6}-15x^{5}+50x^{4}+35x^{4}-175x^{3}-50x^{3}+250x^{2}+24x^{2}-120x$$

Combine 50x^{4} and 35x^{4} to get 85x^{4}.

$$x^{6}-15x^{5}+85x^{4}-175x^{3}-50x^{3}+250x^{2}+24x^{2}-120x$$

Combine -175x^{3} and -50x^{3} to get -225x^{3}.

$$x^{6}-15x^{5}+85x^{4}-225x^{3}+250x^{2}+24x^{2}-120x$$

Combine 250x^{2} and 24x^{2} to get 274x^{2}.

$$x^{6}-15x^{5}+85x^{4}-225x^{3}+274x^{2}-120x$$