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

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

Evaluate

$$\left(3-4x\right)\left(x-3\right)$$

Solution Steps

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

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

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

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

Use the distributive property to multiply -2 by 3x-2.

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

Apply the distributive property by multiplying each term of -6x+4 by each term of x-3.

$$2x^{2}-7x+3-6x^{2}+18x+4x-12$$

Combine 18x and 4x to get 22x.

$$2x^{2}-7x+3-6x^{2}+22x-12$$

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

$$-4x^{2}-7x+3+22x-12$$

Combine -7x and 22x to get 15x.

$$-4x^{2}+15x+3-12$$

Subtract 12 from 3 to get -9.

$$-4x^{2}+15x-9$$

Expand

$$-4x^{2}+15x-9$$

Solution Steps

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

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

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

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

Use the distributive property to multiply -2 by 3x-2.

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

Apply the distributive property by multiplying each term of -6x+4 by each term of x-3.

$$2x^{2}-7x+3-6x^{2}+18x+4x-12$$

Combine 18x and 4x to get 22x.

$$2x^{2}-7x+3-6x^{2}+22x-12$$

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

$$-4x^{2}-7x+3+22x-12$$

Combine -7x and 22x to get 15x.

$$-4x^{2}+15x+3-12$$

Subtract 12 from 3 to get -9.

$$-4x^{2}+15x-9$$