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

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

Evaluate

$$5x-1$$

Solution Steps

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

$$x^{2}-2x+3x-6-\left(x+1\right)\left(x-5\right)$$

Combine -2x and 3x to get x.

$$x^{2}+x-6-\left(x+1\right)\left(x-5\right)$$

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

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

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

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

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

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

The opposite of -4x is 4x.

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

The opposite of -5 is 5.

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

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

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

Combine x and 4x to get 5x.

$$5x-6+5$$

Add -6 and 5 to get -1.

$$5x-1$$

Expand

$$5x-1$$

Solution Steps

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

$$x^{2}-2x+3x-6-\left(x+1\right)\left(x-5\right)$$

Combine -2x and 3x to get x.

$$x^{2}+x-6-\left(x+1\right)\left(x-5\right)$$

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

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

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

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

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

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

The opposite of -4x is 4x.

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

The opposite of -5 is 5.

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

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

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

Combine x and 4x to get 5x.

$$5x-6+5$$

Add -6 and 5 to get -1.

$$5x-1$$