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

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

Evaluate

$$5$$

Solution Steps

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

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

Combine x and -3x to get -2x.

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

Apply the distributive property by multiplying each term of x+2 by each term of x-4.

$$x^{2}-2x-3-\left(x^{2}-4x+2x-8\right)$$

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

$$x^{2}-2x-3-\left(x^{2}-2x-8\right)$$

To find the opposite of x^{2}-2x-8, find the opposite of each term.

$$x^{2}-2x-3-x^{2}-\left(-2x\right)-\left(-8\right)$$

The opposite of -2x is 2x.

$$x^{2}-2x-3-x^{2}+2x-\left(-8\right)$$

The opposite of -8 is 8.

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

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

$$-2x-3+2x+8$$

Combine -2x and 2x to get 0.

$$-3+8$$

Add -3 and 8 to get 5.

$$5$$

Factor

$$5$$