Solve (x+1)(x-2)(x+3)(x-5)-15

$$(x+1)(x-2)(x+3)(x-5)-15$$

Evaluate

$$\left(x-5\right)\left(x-2\right)\left(x+1\right)\left(x+3\right)-15$$

Solution Steps

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

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

Combine -2x and x to get -x.

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

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

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

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

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

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

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

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

$$x^{4}-5x^{3}+2x^{3}-10x^{2}-5x^{2}+25x-6x+30-15$$

Combine -5x^{3} and 2x^{3} to get -3x^{3}.

$$x^{4}-3x^{3}-10x^{2}-5x^{2}+25x-6x+30-15$$

Combine -10x^{2} and -5x^{2} to get -15x^{2}.

$$x^{4}-3x^{3}-15x^{2}+25x-6x+30-15$$

Combine 25x and -6x to get 19x.

$$x^{4}-3x^{3}-15x^{2}+19x+30-15$$

Subtract 15 from 30 to get 15.

$$x^{4}-3x^{3}-15x^{2}+19x+15$$

Expand

$$x^{4}-3x^{3}-15x^{2}+19x+15$$

Solution Steps

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

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

Combine -2x and x to get -x.

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

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

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

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

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

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

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

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

$$x^{4}-5x^{3}+2x^{3}-10x^{2}-5x^{2}+25x-6x+30-15$$

Combine -5x^{3} and 2x^{3} to get -3x^{3}.

$$x^{4}-3x^{3}-10x^{2}-5x^{2}+25x-6x+30-15$$

Combine -10x^{2} and -5x^{2} to get -15x^{2}.

$$x^{4}-3x^{3}-15x^{2}+25x-6x+30-15$$

Combine 25x and -6x to get 19x.

$$x^{4}-3x^{3}-15x^{2}+19x+30-15$$

Subtract 15 from 30 to get 15.

$$x^{4}-3x^{3}-15x^{2}+19x+15$$