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

$$(x-4)(x-2)-(x-1) \times (x-3)$$

Evaluate

$$5-2x$$

Solution Steps

Apply the distributive property by multiplying each term of x-4 by each term of x-2.

$$x^{2}-2x-4x+8-\left(x-1\right)\left(x-3\right)$$

Combine -2x and -4x to get -6x.

$$x^{2}-6x+8-\left(x-1\right)\left(x-3\right)$$

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

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

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

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

To find the opposite of x^{2}-4x+3, find the opposite of each term.

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

The opposite of -4x is 4x.

$$x^{2}-6x+8-x^{2}+4x-3$$

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

$$-6x+8+4x-3$$

Combine -6x and 4x to get -2x.

$$-2x+8-3$$

Subtract 3 from 8 to get 5.

$$-2x+5$$

Expand

$$5-2x$$

Solution Steps

Apply the distributive property by multiplying each term of x-4 by each term of x-2.

$$x^{2}-2x-4x+8-\left(x-1\right)\left(x-3\right)$$

Combine -2x and -4x to get -6x.

$$x^{2}-6x+8-\left(x-1\right)\left(x-3\right)$$

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

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

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

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

To find the opposite of x^{2}-4x+3, find the opposite of each term.

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

The opposite of -4x is 4x.

$$x^{2}-6x+8-x^{2}+4x-3$$

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

$$-6x+8+4x-3$$

Combine -6x and 4x to get -2x.

$$-2x+8-3$$

Subtract 3 from 8 to get 5.

$$-2x+5$$