Solve (2x-1)(2x+7)-(2x-1)(x-3)

$$( 2 x - 1 ) ( 2 x + 7 ) - ( 2 x - 1 ) ( x - 3 )$$

Evaluate

$$\left(2x-1\right)\left(x+10\right)$$

Solution Steps

Apply the distributive property by multiplying each term of 2x-1 by each term of 2x+7.

$$4x^{2}+14x-2x-7-\left(2x-1\right)\left(x-3\right)$$

Combine 14x and -2x to get 12x.

$$4x^{2}+12x-7-\left(2x-1\right)\left(x-3\right)$$

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

$$4x^{2}+12x-7-\left(2x^{2}-6x-x+3\right)$$

Combine -6x and -x to get -7x.

$$4x^{2}+12x-7-\left(2x^{2}-7x+3\right)$$

To find the opposite of 2x^{2}-7x+3, find the opposite of each term.

$$4x^{2}+12x-7-2x^{2}-\left(-7x\right)-3$$

The opposite of -7x is 7x.

$$4x^{2}+12x-7-2x^{2}+7x-3$$

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

$$2x^{2}+12x-7+7x-3$$

Combine 12x and 7x to get 19x.

$$2x^{2}+19x-7-3$$

Subtract 3 from -7 to get -10.

$$2x^{2}+19x-10$$

Expand

$$2x^{2}+19x-10$$

Solution Steps

Apply the distributive property by multiplying each term of 2x-1 by each term of 2x+7.

$$4x^{2}+14x-2x-7-\left(2x-1\right)\left(x-3\right)$$

Combine 14x and -2x to get 12x.

$$4x^{2}+12x-7-\left(2x-1\right)\left(x-3\right)$$

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

$$4x^{2}+12x-7-\left(2x^{2}-6x-x+3\right)$$

Combine -6x and -x to get -7x.

$$4x^{2}+12x-7-\left(2x^{2}-7x+3\right)$$

To find the opposite of 2x^{2}-7x+3, find the opposite of each term.

$$4x^{2}+12x-7-2x^{2}-\left(-7x\right)-3$$

The opposite of -7x is 7x.

$$4x^{2}+12x-7-2x^{2}+7x-3$$

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

$$2x^{2}+12x-7+7x-3$$

Combine 12x and 7x to get 19x.

$$2x^{2}+19x-7-3$$

Subtract 3 from -7 to get -10.

$$2x^{2}+19x-10$$