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

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

Evaluate

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

Solution Steps

Use the distributive property to multiply -2 by x+1.

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

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

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

Combine 4x and -2x to get 2x.

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

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

$$\left(-2x^{3}-6x^{2}+2x^{2}+6x+4x+12\right)\left(x-4\right)$$

Combine -6x^{2} and 2x^{2} to get -4x^{2}.

$$\left(-2x^{3}-4x^{2}+6x+4x+12\right)\left(x-4\right)$$

Combine 6x and 4x to get 10x.

$$\left(-2x^{3}-4x^{2}+10x+12\right)\left(x-4\right)$$

Apply the distributive property by multiplying each term of -2x^{3}-4x^{2}+10x+12 by each term of x-4.

$$-2x^{4}+8x^{3}-4x^{3}+16x^{2}+10x^{2}-40x+12x-48$$

Combine 8x^{3} and -4x^{3} to get 4x^{3}.

$$-2x^{4}+4x^{3}+16x^{2}+10x^{2}-40x+12x-48$$

Combine 16x^{2} and 10x^{2} to get 26x^{2}.

$$-2x^{4}+4x^{3}+26x^{2}-40x+12x-48$$

Combine -40x and 12x to get -28x.

$$-2x^{4}+4x^{3}+26x^{2}-28x-48$$

Expand

$$-2x^{4}+4x^{3}+26x^{2}-28x-48$$

Solution Steps

Use the distributive property to multiply -2 by x+1.

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

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

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

Combine 4x and -2x to get 2x.

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

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

$$\left(-2x^{3}-6x^{2}+2x^{2}+6x+4x+12\right)\left(x-4\right)$$

Combine -6x^{2} and 2x^{2} to get -4x^{2}.

$$\left(-2x^{3}-4x^{2}+6x+4x+12\right)\left(x-4\right)$$

Combine 6x and 4x to get 10x.

$$\left(-2x^{3}-4x^{2}+10x+12\right)\left(x-4\right)$$

Apply the distributive property by multiplying each term of -2x^{3}-4x^{2}+10x+12 by each term of x-4.

$$-2x^{4}+8x^{3}-4x^{3}+16x^{2}+10x^{2}-40x+12x-48$$

Combine 8x^{3} and -4x^{3} to get 4x^{3}.

$$-2x^{4}+4x^{3}+16x^{2}+10x^{2}-40x+12x-48$$

Combine 16x^{2} and 10x^{2} to get 26x^{2}.

$$-2x^{4}+4x^{3}+26x^{2}-40x+12x-48$$

Combine -40x and 12x to get -28x.

$$-2x^{4}+4x^{3}+26x^{2}-28x-48$$