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

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

Evaluate

$$-x^{2}+x-1$$

Solution Steps

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

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

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

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

Apply the distributive property by multiplying each term of x-2 by each term of 2x+1.

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

Combine x and -4x to get -3x.

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

To find the opposite of 2x^{2}-3x-2, find the opposite of each term.

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

The opposite of -3x is 3x.

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

The opposite of -2 is 2.

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

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

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

Combine -2x and 3x to get x.

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

Add -3 and 2 to get -1.

$$-x^{2}+x-1$$

Expand

$$-x^{2}+x-1$$

Solution Steps

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

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

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

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

Apply the distributive property by multiplying each term of x-2 by each term of 2x+1.

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

Combine x and -4x to get -3x.

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

To find the opposite of 2x^{2}-3x-2, find the opposite of each term.

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

The opposite of -3x is 3x.

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

The opposite of -2 is 2.

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

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

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

Combine -2x and 3x to get x.

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

Add -3 and 2 to get -1.

$$-x^{2}+x-1$$