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

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

Evaluate

$$4x-10$$

Solution Steps

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

$$x^{2}-3x+2x-6-\left(x-1\right)\left(x-4\right)$$

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

$$x^{2}-x-6-\left(x-1\right)\left(x-4\right)$$

Apply the distributive property by multiplying each term of x-1 by each term of x-4.

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

Combine -4x and -x to get -5x.

$$x^{2}-x-6-\left(x^{2}-5x+4\right)$$

To find the opposite of x^{2}-5x+4, find the opposite of each term.

$$x^{2}-x-6-x^{2}-\left(-5x\right)-4$$

The opposite of -5x is 5x.

$$x^{2}-x-6-x^{2}+5x-4$$

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

$$-x-6+5x-4$$

Combine -x and 5x to get 4x.

$$4x-6-4$$

Subtract 4 from -6 to get -10.

$$4x-10$$

Expand

$$4x-10$$

Solution Steps

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

$$x^{2}-3x+2x-6-\left(x-1\right)\left(x-4\right)$$

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

$$x^{2}-x-6-\left(x-1\right)\left(x-4\right)$$

Apply the distributive property by multiplying each term of x-1 by each term of x-4.

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

Combine -4x and -x to get -5x.

$$x^{2}-x-6-\left(x^{2}-5x+4\right)$$

To find the opposite of x^{2}-5x+4, find the opposite of each term.

$$x^{2}-x-6-x^{2}-\left(-5x\right)-4$$

The opposite of -5x is 5x.

$$x^{2}-x-6-x^{2}+5x-4$$

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

$$-x-6+5x-4$$

Combine -x and 5x to get 4x.

$$4x-6-4$$

Subtract 4 from -6 to get -10.

$$4x-10$$