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

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

Evaluate

$$2x^{2}$$

Solution Steps

Apply the distributive property by multiplying each term of 3x-5 by each term of 4x-5.

$$12x^{2}-15x-20x+25-\left(2x-5\right)\left(5x-5\right)$$

Combine -15x and -20x to get -35x.

$$12x^{2}-35x+25-\left(2x-5\right)\left(5x-5\right)$$

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

$$12x^{2}-35x+25-\left(10x^{2}-10x-25x+25\right)$$

Combine -10x and -25x to get -35x.

$$12x^{2}-35x+25-\left(10x^{2}-35x+25\right)$$

To find the opposite of 10x^{2}-35x+25, find the opposite of each term.

$$12x^{2}-35x+25-10x^{2}-\left(-35x\right)-25$$

The opposite of -35x is 35x.

$$12x^{2}-35x+25-10x^{2}+35x-25$$

Combine 12x^{2} and -10x^{2} to get 2x^{2}.

$$2x^{2}-35x+25+35x-25$$

Combine -35x and 35x to get 0.

$$2x^{2}+25-25$$

Subtract 25 from 25 to get 0.

$$2x^{2}$$

Expand

$$2x^{2}$$

Solution Steps

Apply the distributive property by multiplying each term of 3x-5 by each term of 4x-5.

$$12x^{2}-15x-20x+25-\left(2x-5\right)\left(5x-5\right)$$

Combine -15x and -20x to get -35x.

$$12x^{2}-35x+25-\left(2x-5\right)\left(5x-5\right)$$

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

$$12x^{2}-35x+25-\left(10x^{2}-10x-25x+25\right)$$

Combine -10x and -25x to get -35x.

$$12x^{2}-35x+25-\left(10x^{2}-35x+25\right)$$

To find the opposite of 10x^{2}-35x+25, find the opposite of each term.

$$12x^{2}-35x+25-10x^{2}-\left(-35x\right)-25$$

The opposite of -35x is 35x.

$$12x^{2}-35x+25-10x^{2}+35x-25$$

Combine 12x^{2} and -10x^{2} to get 2x^{2}.

$$2x^{2}-35x+25+35x-25$$

Combine -35x and 35x to get 0.

$$2x^{2}+25-25$$

Subtract 25 from 25 to get 0.

$$2x^{2}$$