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

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

Evaluate

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

Solution Steps

Apply the distributive property by multiplying each term of x+4 by each term of x+2.

$$\left(x^{2}+2x+4x+8\right)\left(x-1\right)\left(x-3\right)$$

Combine 2x and 4x to get 6x.

$$\left(x^{2}+6x+8\right)\left(x-1\right)\left(x-3\right)$$

Apply the distributive property by multiplying each term of x^{2}+6x+8 by each term of x-1.

$$\left(x^{3}-x^{2}+6x^{2}-6x+8x-8\right)\left(x-3\right)$$

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

$$\left(x^{3}+5x^{2}-6x+8x-8\right)\left(x-3\right)$$

Combine -6x and 8x to get 2x.

$$\left(x^{3}+5x^{2}+2x-8\right)\left(x-3\right)$$

Apply the distributive property by multiplying each term of x^{3}+5x^{2}+2x-8 by each term of x-3.

$$x^{4}-3x^{3}+5x^{3}-15x^{2}+2x^{2}-6x-8x+24$$

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

$$x^{4}+2x^{3}-15x^{2}+2x^{2}-6x-8x+24$$

Combine -15x^{2} and 2x^{2} to get -13x^{2}.

$$x^{4}+2x^{3}-13x^{2}-6x-8x+24$$

Combine -6x and -8x to get -14x.

$$x^{4}+2x^{3}-13x^{2}-14x+24$$

Expand

$$x^{4}+2x^{3}-13x^{2}-14x+24$$

Solution Steps

Apply the distributive property by multiplying each term of x+4 by each term of x+2.

$$\left(x^{2}+2x+4x+8\right)\left(x-1\right)\left(x-3\right)$$

Combine 2x and 4x to get 6x.

$$\left(x^{2}+6x+8\right)\left(x-1\right)\left(x-3\right)$$

Apply the distributive property by multiplying each term of x^{2}+6x+8 by each term of x-1.

$$\left(x^{3}-x^{2}+6x^{2}-6x+8x-8\right)\left(x-3\right)$$

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

$$\left(x^{3}+5x^{2}-6x+8x-8\right)\left(x-3\right)$$

Combine -6x and 8x to get 2x.

$$\left(x^{3}+5x^{2}+2x-8\right)\left(x-3\right)$$

Apply the distributive property by multiplying each term of x^{3}+5x^{2}+2x-8 by each term of x-3.

$$x^{4}-3x^{3}+5x^{3}-15x^{2}+2x^{2}-6x-8x+24$$

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

$$x^{4}+2x^{3}-15x^{2}+2x^{2}-6x-8x+24$$

Combine -15x^{2} and 2x^{2} to get -13x^{2}.

$$x^{4}+2x^{3}-13x^{2}-6x-8x+24$$

Combine -6x and -8x to get -14x.

$$x^{4}+2x^{3}-13x^{2}-14x+24$$