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

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

Evaluate

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

Solution Steps

Apply the distributive property by multiplying each term of x+1 by each term of x+3.

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

Combine 3x and x to get 4x.

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

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

$$\left(x^{3}-4x^{2}+4x^{2}-16x+3x-12\right)\left(x-2\right)$$

Combine -4x^{2} and 4x^{2} to get 0.

$$\left(x^{3}-16x+3x-12\right)\left(x-2\right)$$

Combine -16x and 3x to get -13x.

$$\left(x^{3}-13x-12\right)\left(x-2\right)$$

Apply the distributive property by multiplying each term of x^{3}-13x-12 by each term of x-2.

$$x^{4}-2x^{3}-13x^{2}+26x-12x+24$$

Combine 26x and -12x 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+1 by each term of x+3.

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

Combine 3x and x to get 4x.

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

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

$$\left(x^{3}-4x^{2}+4x^{2}-16x+3x-12\right)\left(x-2\right)$$

Combine -4x^{2} and 4x^{2} to get 0.

$$\left(x^{3}-16x+3x-12\right)\left(x-2\right)$$

Combine -16x and 3x to get -13x.

$$\left(x^{3}-13x-12\right)\left(x-2\right)$$

Apply the distributive property by multiplying each term of x^{3}-13x-12 by each term of x-2.

$$x^{4}-2x^{3}-13x^{2}+26x-12x+24$$

Combine 26x and -12x to get 14x.

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