Solve -(x+7)(x-1)-(2x+2)(x+2)

$$-(x+7)(x-1)-(2x+2)(x+2)$$

Evaluate

$$3-12x-3x^{2}$$

Solution Steps

To find the opposite of x+7, find the opposite of each term.

$$\left(-x-7\right)\left(x-1\right)-\left(2x+2\right)\left(x+2\right)$$

Apply the distributive property by multiplying each term of -x-7 by each term of x-1.

$$-x^{2}+x-7x+7-\left(2x+2\right)\left(x+2\right)$$

Combine x and -7x to get -6x.

$$-x^{2}-6x+7-\left(2x+2\right)\left(x+2\right)$$

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

$$-x^{2}-6x+7-\left(2x^{2}+4x+2x+4\right)$$

Combine 4x and 2x to get 6x.

$$-x^{2}-6x+7-\left(2x^{2}+6x+4\right)$$

To find the opposite of 2x^{2}+6x+4, find the opposite of each term.

$$-x^{2}-6x+7-2x^{2}-6x-4$$

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

$$-3x^{2}-6x+7-6x-4$$

Combine -6x and -6x to get -12x.

$$-3x^{2}-12x+7-4$$

Subtract 4 from 7 to get 3.

$$-3x^{2}-12x+3$$

Expand

$$3-12x-3x^{2}$$

Solution Steps

To find the opposite of x+7, find the opposite of each term.

$$\left(-x-7\right)\left(x-1\right)-\left(2x+2\right)\left(x+2\right)$$

Apply the distributive property by multiplying each term of -x-7 by each term of x-1.

$$-x^{2}+x-7x+7-\left(2x+2\right)\left(x+2\right)$$

Combine x and -7x to get -6x.

$$-x^{2}-6x+7-\left(2x+2\right)\left(x+2\right)$$

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

$$-x^{2}-6x+7-\left(2x^{2}+4x+2x+4\right)$$

Combine 4x and 2x to get 6x.

$$-x^{2}-6x+7-\left(2x^{2}+6x+4\right)$$

To find the opposite of 2x^{2}+6x+4, find the opposite of each term.

$$-x^{2}-6x+7-2x^{2}-6x-4$$

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

$$-3x^{2}-6x+7-6x-4$$

Combine -6x and -6x to get -12x.

$$-3x^{2}-12x+7-4$$

Subtract 4 from 7 to get 3.

$$-3x^{2}-12x+3$$