Solve (x-3)(x+4)-(x+5)(x+1)=

$$(x-3)(x+4)-(x+5)(x+1)=$$

Evaluate

$$-5x-17$$

Solution Steps

Apply the distributive property by multiplying each term of x-3 by each term of x+4.

$$x^{2}+4x-3x-12-\left(x+5\right)\left(x+1\right)$$

Combine 4x and -3x to get x.

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

Apply the distributive property by multiplying each term of x+5 by each term of x+1.

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

Combine x and 5x to get 6x.

$$x^{2}+x-12-\left(x^{2}+6x+5\right)$$

To find the opposite of x^{2}+6x+5, find the opposite of each term.

$$x^{2}+x-12-x^{2}-6x-5$$

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

$$x-12-6x-5$$

Combine x and -6x to get -5x.

$$-5x-12-5$$

Subtract 5 from -12 to get -17.

$$-5x-17$$

Expand

$$-5x-17$$

Solution Steps

Apply the distributive property by multiplying each term of x-3 by each term of x+4.

$$x^{2}+4x-3x-12-\left(x+5\right)\left(x+1\right)$$

Combine 4x and -3x to get x.

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

Apply the distributive property by multiplying each term of x+5 by each term of x+1.

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

Combine x and 5x to get 6x.

$$x^{2}+x-12-\left(x^{2}+6x+5\right)$$

To find the opposite of x^{2}+6x+5, find the opposite of each term.

$$x^{2}+x-12-x^{2}-6x-5$$

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

$$x-12-6x-5$$

Combine x and -6x to get -5x.

$$-5x-12-5$$

Subtract 5 from -12 to get -17.

$$-5x-17$$