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

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

Evaluate

$$-3x^{2}+7x-7$$

Solution Steps

Apply the distributive property by multiplying each term of x-2 by each term of x+5.

$$x^{2}+5x-2x-10-\left(2x-3\right)\left(2x+1\right)$$

Combine 5x and -2x to get 3x.

$$x^{2}+3x-10-\left(2x-3\right)\left(2x+1\right)$$

Apply the distributive property by multiplying each term of 2x-3 by each term of 2x+1.

$$x^{2}+3x-10-\left(4x^{2}+2x-6x-3\right)$$

Combine 2x and -6x to get -4x.

$$x^{2}+3x-10-\left(4x^{2}-4x-3\right)$$

To find the opposite of 4x^{2}-4x-3, find the opposite of each term.

$$x^{2}+3x-10-4x^{2}-\left(-4x\right)-\left(-3\right)$$

The opposite of -4x is 4x.

$$x^{2}+3x-10-4x^{2}+4x-\left(-3\right)$$

The opposite of -3 is 3.

$$x^{2}+3x-10-4x^{2}+4x+3$$

Combine x^{2} and -4x^{2} to get -3x^{2}.

$$-3x^{2}+3x-10+4x+3$$

Combine 3x and 4x to get 7x.

$$-3x^{2}+7x-10+3$$

Add -10 and 3 to get -7.

$$-3x^{2}+7x-7$$

Expand

$$-3x^{2}+7x-7$$

Solution Steps

Apply the distributive property by multiplying each term of x-2 by each term of x+5.

$$x^{2}+5x-2x-10-\left(2x-3\right)\left(2x+1\right)$$

Combine 5x and -2x to get 3x.

$$x^{2}+3x-10-\left(2x-3\right)\left(2x+1\right)$$

Apply the distributive property by multiplying each term of 2x-3 by each term of 2x+1.

$$x^{2}+3x-10-\left(4x^{2}+2x-6x-3\right)$$

Combine 2x and -6x to get -4x.

$$x^{2}+3x-10-\left(4x^{2}-4x-3\right)$$

To find the opposite of 4x^{2}-4x-3, find the opposite of each term.

$$x^{2}+3x-10-4x^{2}-\left(-4x\right)-\left(-3\right)$$

The opposite of -4x is 4x.

$$x^{2}+3x-10-4x^{2}+4x-\left(-3\right)$$

The opposite of -3 is 3.

$$x^{2}+3x-10-4x^{2}+4x+3$$

Combine x^{2} and -4x^{2} to get -3x^{2}.

$$-3x^{2}+3x-10+4x+3$$

Combine 3x and 4x to get 7x.

$$-3x^{2}+7x-10+3$$

Add -10 and 3 to get -7.

$$-3x^{2}+7x-7$$