Solve (3x+1)(2x-3)-(6x-8)(x-4)

$$( 3 x + 1 ) ( 2 x - 3 ) - ( 6 x - 8 ) ( x - 4 )$$

Evaluate

$$25x-35$$

Solution Steps

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

$$6x^{2}-9x+2x-3-\left(6x-8\right)\left(x-4\right)$$

Combine -9x and 2x to get -7x.

$$6x^{2}-7x-3-\left(6x-8\right)\left(x-4\right)$$

Apply the distributive property by multiplying each term of 6x-8 by each term of x-4.

$$6x^{2}-7x-3-\left(6x^{2}-24x-8x+32\right)$$

Combine -24x and -8x to get -32x.

$$6x^{2}-7x-3-\left(6x^{2}-32x+32\right)$$

To find the opposite of 6x^{2}-32x+32, find the opposite of each term.

$$6x^{2}-7x-3-6x^{2}-\left(-32x\right)-32$$

The opposite of -32x is 32x.

$$6x^{2}-7x-3-6x^{2}+32x-32$$

Combine 6x^{2} and -6x^{2} to get 0.

$$-7x-3+32x-32$$

Combine -7x and 32x to get 25x.

$$25x-3-32$$

Subtract 32 from -3 to get -35.

$$25x-35$$

Expand

$$25x-35$$

Solution Steps

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

$$6x^{2}-9x+2x-3-\left(6x-8\right)\left(x-4\right)$$

Combine -9x and 2x to get -7x.

$$6x^{2}-7x-3-\left(6x-8\right)\left(x-4\right)$$

Apply the distributive property by multiplying each term of 6x-8 by each term of x-4.

$$6x^{2}-7x-3-\left(6x^{2}-24x-8x+32\right)$$

Combine -24x and -8x to get -32x.

$$6x^{2}-7x-3-\left(6x^{2}-32x+32\right)$$

To find the opposite of 6x^{2}-32x+32, find the opposite of each term.

$$6x^{2}-7x-3-6x^{2}-\left(-32x\right)-32$$

The opposite of -32x is 32x.

$$6x^{2}-7x-3-6x^{2}+32x-32$$

Combine 6x^{2} and -6x^{2} to get 0.

$$-7x-3+32x-32$$

Combine -7x and 32x to get 25x.

$$25x-3-32$$

Subtract 32 from -3 to get -35.

$$25x-35$$