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

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

Evaluate

$$14-2x$$

Solution Steps

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

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

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

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

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

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

Combine -4x and 3x to get -x.

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

To find the opposite of x^{2}-x-12, find the opposite of each term.

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

The opposite of -x is x.

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

The opposite of -12 is 12.

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

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

$$-3x+2+x+12$$

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

$$-2x+2+12$$

Add 2 and 12 to get 14.

$$-2x+14$$

Expand

$$14-2x$$

Solution Steps

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

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

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

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

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

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

Combine -4x and 3x to get -x.

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

To find the opposite of x^{2}-x-12, find the opposite of each term.

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

The opposite of -x is x.

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

The opposite of -12 is 12.

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

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

$$-3x+2+x+12$$

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

$$-2x+2+12$$

Add 2 and 12 to get 14.

$$-2x+14$$