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

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

Evaluate

$$-7x-1$$

Solution Steps

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

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

Combine -x and -2x to get -3x.

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

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

$$x^{2}-3x+2+x^{2}-2x+3x-6-\left(2x-1\right)\left(x+3\right)$$

Combine -2x and 3x to get x.

$$x^{2}-3x+2+x^{2}+x-6-\left(2x-1\right)\left(x+3\right)$$

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

$$2x^{2}-3x+2+x-6-\left(2x-1\right)\left(x+3\right)$$

Combine -3x and x to get -2x.

$$2x^{2}-2x+2-6-\left(2x-1\right)\left(x+3\right)$$

Subtract 6 from 2 to get -4.

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

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

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

Combine 6x and -x to get 5x.

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

To find the opposite of 2x^{2}+5x-3, find the opposite of each term.

$$2x^{2}-2x-4-2x^{2}-5x-\left(-3\right)$$

The opposite of -3 is 3.

$$2x^{2}-2x-4-2x^{2}-5x+3$$

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

$$-2x-4-5x+3$$

Combine -2x and -5x to get -7x.

$$-7x-4+3$$

Add -4 and 3 to get -1.

$$-7x-1$$

Expand

$$-7x-1$$

Solution Steps

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

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

Combine -x and -2x to get -3x.

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

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

$$x^{2}-3x+2+x^{2}-2x+3x-6-\left(2x-1\right)\left(x+3\right)$$

Combine -2x and 3x to get x.

$$x^{2}-3x+2+x^{2}+x-6-\left(2x-1\right)\left(x+3\right)$$

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

$$2x^{2}-3x+2+x-6-\left(2x-1\right)\left(x+3\right)$$

Combine -3x and x to get -2x.

$$2x^{2}-2x+2-6-\left(2x-1\right)\left(x+3\right)$$

Subtract 6 from 2 to get -4.

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

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

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

Combine 6x and -x to get 5x.

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

To find the opposite of 2x^{2}+5x-3, find the opposite of each term.

$$2x^{2}-2x-4-2x^{2}-5x-\left(-3\right)$$

The opposite of -3 is 3.

$$2x^{2}-2x-4-2x^{2}-5x+3$$

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

$$-2x-4-5x+3$$

Combine -2x and -5x to get -7x.

$$-7x-4+3$$

Add -4 and 3 to get -1.

$$-7x-1$$