Solve (5x-4)(2x-2)-(3x+1)(x-1)

$$(5x-4)(2x-2)-(3x+1)(x-1)$$

Evaluate

$$\left(x-1\right)\left(7x-9\right)$$

Solution Steps

Apply the distributive property by multiplying each term of 5x-4 by each term of 2x-2.

$$10x^{2}-10x-8x+8-\left(3x+1\right)\left(x-1\right)$$

Combine -10x and -8x to get -18x.

$$10x^{2}-18x+8-\left(3x+1\right)\left(x-1\right)$$

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

$$10x^{2}-18x+8-\left(3x^{2}-3x+x-1\right)$$

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

$$10x^{2}-18x+8-\left(3x^{2}-2x-1\right)$$

To find the opposite of 3x^{2}-2x-1, find the opposite of each term.

$$10x^{2}-18x+8-3x^{2}-\left(-2x\right)-\left(-1\right)$$

The opposite of -2x is 2x.

$$10x^{2}-18x+8-3x^{2}+2x-\left(-1\right)$$

The opposite of -1 is 1.

$$10x^{2}-18x+8-3x^{2}+2x+1$$

Combine 10x^{2} and -3x^{2} to get 7x^{2}.

$$7x^{2}-18x+8+2x+1$$

Combine -18x and 2x to get -16x.

$$7x^{2}-16x+8+1$$

Add 8 and 1 to get 9.

$$7x^{2}-16x+9$$

Expand

$$7x^{2}-16x+9$$

Solution Steps

Apply the distributive property by multiplying each term of 5x-4 by each term of 2x-2.

$$10x^{2}-10x-8x+8-\left(3x+1\right)\left(x-1\right)$$

Combine -10x and -8x to get -18x.

$$10x^{2}-18x+8-\left(3x+1\right)\left(x-1\right)$$

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

$$10x^{2}-18x+8-\left(3x^{2}-3x+x-1\right)$$

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

$$10x^{2}-18x+8-\left(3x^{2}-2x-1\right)$$

To find the opposite of 3x^{2}-2x-1, find the opposite of each term.

$$10x^{2}-18x+8-3x^{2}-\left(-2x\right)-\left(-1\right)$$

The opposite of -2x is 2x.

$$10x^{2}-18x+8-3x^{2}+2x-\left(-1\right)$$

The opposite of -1 is 1.

$$10x^{2}-18x+8-3x^{2}+2x+1$$

Combine 10x^{2} and -3x^{2} to get 7x^{2}.

$$7x^{2}-18x+8+2x+1$$

Combine -18x and 2x to get -16x.

$$7x^{2}-16x+8+1$$

Add 8 and 1 to get 9.

$$7x^{2}-16x+9$$