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

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

Evaluate

$$8x^{2}-16x+6$$

Solution Steps

Apply the distributive property by multiplying each term of 2x-3 by each term of 5x-1.

$$10x^{2}-2x-15x+3-\left(2x-3\right)\left(x+1\right)$$

Combine -2x and -15x to get -17x.

$$10x^{2}-17x+3-\left(2x-3\right)\left(x+1\right)$$

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

$$10x^{2}-17x+3-\left(2x^{2}+2x-3x-3\right)$$

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

$$10x^{2}-17x+3-\left(2x^{2}-x-3\right)$$

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

$$10x^{2}-17x+3-2x^{2}-\left(-x\right)-\left(-3\right)$$

The opposite of -x is x.

$$10x^{2}-17x+3-2x^{2}+x-\left(-3\right)$$

The opposite of -3 is 3.

$$10x^{2}-17x+3-2x^{2}+x+3$$

Combine 10x^{2} and -2x^{2} to get 8x^{2}.

$$8x^{2}-17x+3+x+3$$

Combine -17x and x to get -16x.

$$8x^{2}-16x+3+3$$

Add 3 and 3 to get 6.

$$8x^{2}-16x+6$$

Expand

$$8x^{2}-16x+6$$

Solution Steps

Apply the distributive property by multiplying each term of 2x-3 by each term of 5x-1.

$$10x^{2}-2x-15x+3-\left(2x-3\right)\left(x+1\right)$$

Combine -2x and -15x to get -17x.

$$10x^{2}-17x+3-\left(2x-3\right)\left(x+1\right)$$

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

$$10x^{2}-17x+3-\left(2x^{2}+2x-3x-3\right)$$

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

$$10x^{2}-17x+3-\left(2x^{2}-x-3\right)$$

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

$$10x^{2}-17x+3-2x^{2}-\left(-x\right)-\left(-3\right)$$

The opposite of -x is x.

$$10x^{2}-17x+3-2x^{2}+x-\left(-3\right)$$

The opposite of -3 is 3.

$$10x^{2}-17x+3-2x^{2}+x+3$$

Combine 10x^{2} and -2x^{2} to get 8x^{2}.

$$8x^{2}-17x+3+x+3$$

Combine -17x and x to get -16x.

$$8x^{2}-16x+3+3$$

Add 3 and 3 to get 6.

$$8x^{2}-16x+6$$