Solve (x-1)(x+1)(x+3)(x+5)+12

$$( x - 1 ) ( x + 1 ) ( x + 3 ) ( x + 5 ) + 12$$

Evaluate

$$\left(x+3\right)\left(x+5\right)\left(x^{2}-1\right)+12$$

Solution Steps

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

$$\left(x^{2}+x-x-1\right)\left(x+3\right)\left(x+5\right)+12$$

Combine x and -x to get 0.

$$\left(x^{2}-1\right)\left(x+3\right)\left(x+5\right)+12$$

Apply the distributive property by multiplying each term of x^{2}-1 by each term of x+3.

$$\left(x^{3}+3x^{2}-x-3\right)\left(x+5\right)+12$$

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

$$x^{4}+5x^{3}+3x^{3}+15x^{2}-x^{2}-5x-3x-15+12$$

Combine 5x^{3} and 3x^{3} to get 8x^{3}.

$$x^{4}+8x^{3}+15x^{2}-x^{2}-5x-3x-15+12$$

Combine 15x^{2} and -x^{2} to get 14x^{2}.

$$x^{4}+8x^{3}+14x^{2}-5x-3x-15+12$$

Combine -5x and -3x to get -8x.

$$x^{4}+8x^{3}+14x^{2}-8x-15+12$$

Add -15 and 12 to get -3.

$$x^{4}+8x^{3}+14x^{2}-8x-3$$

Expand

$$x^{4}+8x^{3}+14x^{2}-8x-3$$

Solution Steps

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

$$\left(x^{2}+x-x-1\right)\left(x+3\right)\left(x+5\right)+12$$

Combine x and -x to get 0.

$$\left(x^{2}-1\right)\left(x+3\right)\left(x+5\right)+12$$

Apply the distributive property by multiplying each term of x^{2}-1 by each term of x+3.

$$\left(x^{3}+3x^{2}-x-3\right)\left(x+5\right)+12$$

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

$$x^{4}+5x^{3}+3x^{3}+15x^{2}-x^{2}-5x-3x-15+12$$

Combine 5x^{3} and 3x^{3} to get 8x^{3}.

$$x^{4}+8x^{3}+15x^{2}-x^{2}-5x-3x-15+12$$

Combine 15x^{2} and -x^{2} to get 14x^{2}.

$$x^{4}+8x^{3}+14x^{2}-5x-3x-15+12$$

Combine -5x and -3x to get -8x.

$$x^{4}+8x^{3}+14x^{2}-8x-15+12$$

Add -15 and 12 to get -3.

$$x^{4}+8x^{3}+14x^{2}-8x-3$$