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

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

Evaluate

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

Solution Steps

Apply the distributive property by multiplying each term of 3x-1 by each term of 5x+2.

$$15x^{2}+6x-5x-2-\left(5x+2\right)\left(2-x\right)$$

Combine 6x and -5x to get x.

$$15x^{2}+x-2-\left(5x+2\right)\left(2-x\right)$$

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

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

Combine 10x and -2x to get 8x.

$$15x^{2}+x-2-\left(8x-5x^{2}+4\right)$$

To find the opposite of 8x-5x^{2}+4, find the opposite of each term.

$$15x^{2}+x-2-8x-\left(-5x^{2}\right)-4$$

The opposite of -5x^{2} is 5x^{2}.

$$15x^{2}+x-2-8x+5x^{2}-4$$

Combine x and -8x to get -7x.

$$15x^{2}-7x-2+5x^{2}-4$$

Combine 15x^{2} and 5x^{2} to get 20x^{2}.

$$20x^{2}-7x-2-4$$

Subtract 4 from -2 to get -6.

$$20x^{2}-7x-6$$

Expand

$$20x^{2}-7x-6$$

Solution Steps

Apply the distributive property by multiplying each term of 3x-1 by each term of 5x+2.

$$15x^{2}+6x-5x-2-\left(5x+2\right)\left(2-x\right)$$

Combine 6x and -5x to get x.

$$15x^{2}+x-2-\left(5x+2\right)\left(2-x\right)$$

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

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

Combine 10x and -2x to get 8x.

$$15x^{2}+x-2-\left(8x-5x^{2}+4\right)$$

To find the opposite of 8x-5x^{2}+4, find the opposite of each term.

$$15x^{2}+x-2-8x-\left(-5x^{2}\right)-4$$

The opposite of -5x^{2} is 5x^{2}.

$$15x^{2}+x-2-8x+5x^{2}-4$$

Combine x and -8x to get -7x.

$$15x^{2}-7x-2+5x^{2}-4$$

Combine 15x^{2} and 5x^{2} to get 20x^{2}.

$$20x^{2}-7x-2-4$$

Subtract 4 from -2 to get -6.

$$20x^{2}-7x-6$$