Solve (x-2)(x-3)(x-1)(x-4)-15

$$(x-2)(x-3)(x-1)(x-4)-15$$

Evaluate

$$\left(x-4\right)\left(x-3\right)\left(x-2\right)\left(x-1\right)-15$$

Solution Steps

Apply the distributive property by multiplying each term of x-2 by each term of x-3.

$$\left(x^{2}-3x-2x+6\right)\left(x-1\right)\left(x-4\right)-15$$

Combine -3x and -2x to get -5x.

$$\left(x^{2}-5x+6\right)\left(x-1\right)\left(x-4\right)-15$$

Apply the distributive property by multiplying each term of x^{2}-5x+6 by each term of x-1.

$$\left(x^{3}-x^{2}-5x^{2}+5x+6x-6\right)\left(x-4\right)-15$$

Combine -x^{2} and -5x^{2} to get -6x^{2}.

$$\left(x^{3}-6x^{2}+5x+6x-6\right)\left(x-4\right)-15$$

Combine 5x and 6x to get 11x.

$$\left(x^{3}-6x^{2}+11x-6\right)\left(x-4\right)-15$$

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

$$x^{4}-4x^{3}-6x^{3}+24x^{2}+11x^{2}-44x-6x+24-15$$

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

$$x^{4}-10x^{3}+24x^{2}+11x^{2}-44x-6x+24-15$$

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

$$x^{4}-10x^{3}+35x^{2}-44x-6x+24-15$$

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

$$x^{4}-10x^{3}+35x^{2}-50x+24-15$$

Subtract 15 from 24 to get 9.

$$x^{4}-10x^{3}+35x^{2}-50x+9$$

Expand

$$x^{4}-10x^{3}+35x^{2}-50x+9$$

Solution Steps

Apply the distributive property by multiplying each term of x-2 by each term of x-3.

$$\left(x^{2}-3x-2x+6\right)\left(x-1\right)\left(x-4\right)-15$$

Combine -3x and -2x to get -5x.

$$\left(x^{2}-5x+6\right)\left(x-1\right)\left(x-4\right)-15$$

Apply the distributive property by multiplying each term of x^{2}-5x+6 by each term of x-1.

$$\left(x^{3}-x^{2}-5x^{2}+5x+6x-6\right)\left(x-4\right)-15$$

Combine -x^{2} and -5x^{2} to get -6x^{2}.

$$\left(x^{3}-6x^{2}+5x+6x-6\right)\left(x-4\right)-15$$

Combine 5x and 6x to get 11x.

$$\left(x^{3}-6x^{2}+11x-6\right)\left(x-4\right)-15$$

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

$$x^{4}-4x^{3}-6x^{3}+24x^{2}+11x^{2}-44x-6x+24-15$$

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

$$x^{4}-10x^{3}+24x^{2}+11x^{2}-44x-6x+24-15$$

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

$$x^{4}-10x^{3}+35x^{2}-44x-6x+24-15$$

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

$$x^{4}-10x^{3}+35x^{2}-50x+24-15$$

Subtract 15 from 24 to get 9.

$$x^{4}-10x^{3}+35x^{2}-50x+9$$