Solve left(3x-1right)left(x-1right)-left(x+3right)left(1-xright)

$$\left( 3x-1 \right) \left( x-1 \right) - \left( x+3 \right) \left( 1-x \right)$$

Evaluate

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

Solution Steps

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

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

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

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

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

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

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

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

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

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

The opposite of -2x is 2x.

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

The opposite of -x^{2} is x^{2}.

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

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

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

Combine 3x^{2} and x^{2} to get 4x^{2}.

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

Subtract 3 from 1 to get -2.

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

Expand

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

Solution Steps

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

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

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

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

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

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

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

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

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

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

The opposite of -2x is 2x.

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

The opposite of -x^{2} is x^{2}.

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

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

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

Combine 3x^{2} and x^{2} to get 4x^{2}.

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

Subtract 3 from 1 to get -2.

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