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

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

Evaluate

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

Solution Steps

Apply the distributive property by multiplying each term of 4x+3 by each term of x-1.

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

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

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

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

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

Combine -2x and -3x to get -5x.

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

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

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

The opposite of -5x is 5x.

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

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

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

Combine -x and 5x to get 4x.

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

Subtract 3 from -3 to get -6.

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

Expand

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

Solution Steps

Apply the distributive property by multiplying each term of 4x+3 by each term of x-1.

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

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

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

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

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

Combine -2x and -3x to get -5x.

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

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

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

The opposite of -5x is 5x.

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

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

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

Combine -x and 5x to get 4x.

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

Subtract 3 from -3 to get -6.

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