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

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

Evaluate

$$2\left(x-2\right)\left(x-1\right)$$

Solution Steps

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

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

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

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

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

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

Combine -x and 3x to get 2x.

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

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

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

The opposite of -3 is 3.

$$3x^{2}-4x+1-x^{2}-2x+3$$

Combine 3x^{2} and -x^{2} to get 2x^{2}.

$$2x^{2}-4x+1-2x+3$$

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

$$2x^{2}-6x+1+3$$

Add 1 and 3 to get 4.

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

Expand

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

Solution Steps

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

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

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

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

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

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

Combine -x and 3x to get 2x.

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

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

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

The opposite of -3 is 3.

$$3x^{2}-4x+1-x^{2}-2x+3$$

Combine 3x^{2} and -x^{2} to get 2x^{2}.

$$2x^{2}-4x+1-2x+3$$

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

$$2x^{2}-6x+1+3$$

Add 1 and 3 to get 4.

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