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

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

Evaluate

$$6$$

Solution Steps

Apply the distributive property by multiplying each term of x+3 by each term of x-2.

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

Combine -2x and 3x to get x.

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

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

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

Combine -3x and 4x to get x.

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

To find the opposite of x^{2}+x-12, find the opposite of each term.

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

The opposite of -12 is 12.

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

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

$$x-6-x+12$$

Combine x and -x to get 0.

$$-6+12$$

Add -6 and 12 to get 6.

$$6$$

Factor

$$2\times 3$$