Solve (2x+3)(5x-8)-(2x-4)(5x-1)

$$(2x+3)(5x-8)-(2x-4)(5x-1)$$

Evaluate

$$21x-28$$

Solution Steps

Apply the distributive property by multiplying each term of 2x+3 by each term of 5x-8.

$$10x^{2}-16x+15x-24-\left(2x-4\right)\left(5x-1\right)$$

Combine -16x and 15x to get -x.

$$10x^{2}-x-24-\left(2x-4\right)\left(5x-1\right)$$

Apply the distributive property by multiplying each term of 2x-4 by each term of 5x-1.

$$10x^{2}-x-24-\left(10x^{2}-2x-20x+4\right)$$

Combine -2x and -20x to get -22x.

$$10x^{2}-x-24-\left(10x^{2}-22x+4\right)$$

To find the opposite of 10x^{2}-22x+4, find the opposite of each term.

$$10x^{2}-x-24-10x^{2}-\left(-22x\right)-4$$

The opposite of -22x is 22x.

$$10x^{2}-x-24-10x^{2}+22x-4$$

Combine 10x^{2} and -10x^{2} to get 0.

$$-x-24+22x-4$$

Combine -x and 22x to get 21x.

$$21x-24-4$$

Subtract 4 from -24 to get -28.

$$21x-28$$

Expand

$$21x-28$$

Solution Steps

Apply the distributive property by multiplying each term of 2x+3 by each term of 5x-8.

$$10x^{2}-16x+15x-24-\left(2x-4\right)\left(5x-1\right)$$

Combine -16x and 15x to get -x.

$$10x^{2}-x-24-\left(2x-4\right)\left(5x-1\right)$$

Apply the distributive property by multiplying each term of 2x-4 by each term of 5x-1.

$$10x^{2}-x-24-\left(10x^{2}-2x-20x+4\right)$$

Combine -2x and -20x to get -22x.

$$10x^{2}-x-24-\left(10x^{2}-22x+4\right)$$

To find the opposite of 10x^{2}-22x+4, find the opposite of each term.

$$10x^{2}-x-24-10x^{2}-\left(-22x\right)-4$$

The opposite of -22x is 22x.

$$10x^{2}-x-24-10x^{2}+22x-4$$

Combine 10x^{2} and -10x^{2} to get 0.

$$-x-24+22x-4$$

Combine -x and 22x to get 21x.

$$21x-24-4$$

Subtract 4 from -24 to get -28.

$$21x-28$$