Solve (x-1)(x+5)-(x+2)(x-3)

$$(x-1)(x+5)-(x+2)(x-3)$$

Evaluate

$$5x+1$$

Solution Steps

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

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

Combine 5x and -x to get 4x.

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

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

$$x^{2}+4x-5-\left(x^{2}-3x+2x-6\right)$$

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

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

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

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

The opposite of -x is x.

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

The opposite of -6 is 6.

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

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

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

Combine 4x and x to get 5x.

$$5x-5+6$$

Add -5 and 6 to get 1.

$$5x+1$$

Expand

$$5x+1$$

Solution Steps

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

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

Combine 5x and -x to get 4x.

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

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

$$x^{2}+4x-5-\left(x^{2}-3x+2x-6\right)$$

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

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

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

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

The opposite of -x is x.

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

The opposite of -6 is 6.

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

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

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

Combine 4x and x to get 5x.

$$5x-5+6$$

Add -5 and 6 to get 1.

$$5x+1$$