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

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

Evaluate

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

Solution Steps

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

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

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

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

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

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

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

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

Combine 9x and 2x to get 11x.

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

Apply the distributive property by multiplying each term of x^{3}-6x^{2}+11x-6 by each term of x-5.

$$x^{4}-5x^{3}-6x^{3}+30x^{2}+11x^{2}-55x-6x+30$$

Combine -5x^{3} and -6x^{3} to get -11x^{3}.

$$x^{4}-11x^{3}+30x^{2}+11x^{2}-55x-6x+30$$

Combine 30x^{2} and 11x^{2} to get 41x^{2}.

$$x^{4}-11x^{3}+41x^{2}-55x-6x+30$$

Combine -55x and -6x to get -61x.

$$x^{4}-11x^{3}+41x^{2}-61x+30$$

Expand

$$x^{4}-11x^{3}+41x^{2}-61x+30$$

Solution Steps

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

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

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

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

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

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

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

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

Combine 9x and 2x to get 11x.

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

Apply the distributive property by multiplying each term of x^{3}-6x^{2}+11x-6 by each term of x-5.

$$x^{4}-5x^{3}-6x^{3}+30x^{2}+11x^{2}-55x-6x+30$$

Combine -5x^{3} and -6x^{3} to get -11x^{3}.

$$x^{4}-11x^{3}+30x^{2}+11x^{2}-55x-6x+30$$

Combine 30x^{2} and 11x^{2} to get 41x^{2}.

$$x^{4}-11x^{3}+41x^{2}-55x-6x+30$$

Combine -55x and -6x to get -61x.

$$x^{4}-11x^{3}+41x^{2}-61x+30$$