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

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

Evaluate

$$6x^{2}-17x-7$$

Solution Steps

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

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

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

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

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

$$-4x^{2}+4x+3-\left(-10x^{2}-4x+25x+10\right)$$

Combine -4x and 25x to get 21x.

$$-4x^{2}+4x+3-\left(-10x^{2}+21x+10\right)$$

To find the opposite of -10x^{2}+21x+10, find the opposite of each term.

$$-4x^{2}+4x+3-\left(-10x^{2}\right)-21x-10$$

The opposite of -10x^{2} is 10x^{2}.

$$-4x^{2}+4x+3+10x^{2}-21x-10$$

Combine -4x^{2} and 10x^{2} to get 6x^{2}.

$$6x^{2}+4x+3-21x-10$$

Combine 4x and -21x to get -17x.

$$6x^{2}-17x+3-10$$

Subtract 10 from 3 to get -7.

$$6x^{2}-17x-7$$

Expand

$$6x^{2}-17x-7$$

Solution Steps

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

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

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

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

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

$$-4x^{2}+4x+3-\left(-10x^{2}-4x+25x+10\right)$$

Combine -4x and 25x to get 21x.

$$-4x^{2}+4x+3-\left(-10x^{2}+21x+10\right)$$

To find the opposite of -10x^{2}+21x+10, find the opposite of each term.

$$-4x^{2}+4x+3-\left(-10x^{2}\right)-21x-10$$

The opposite of -10x^{2} is 10x^{2}.

$$-4x^{2}+4x+3+10x^{2}-21x-10$$

Combine -4x^{2} and 10x^{2} to get 6x^{2}.

$$6x^{2}+4x+3-21x-10$$

Combine 4x and -21x to get -17x.

$$6x^{2}-17x+3-10$$

Subtract 10 from 3 to get -7.

$$6x^{2}-17x-7$$