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

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

Evaluate

$$2-2x-12x^{2}$$

Solution Steps

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

$$3x^{2}-12x-x+4-\left(3x-1\right)\left(5x-2\right)$$

Combine -12x and -x to get -13x.

$$3x^{2}-13x+4-\left(3x-1\right)\left(5x-2\right)$$

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

$$3x^{2}-13x+4-\left(15x^{2}-6x-5x+2\right)$$

Combine -6x and -5x to get -11x.

$$3x^{2}-13x+4-\left(15x^{2}-11x+2\right)$$

To find the opposite of 15x^{2}-11x+2, find the opposite of each term.

$$3x^{2}-13x+4-15x^{2}-\left(-11x\right)-2$$

The opposite of -11x is 11x.

$$3x^{2}-13x+4-15x^{2}+11x-2$$

Combine 3x^{2} and -15x^{2} to get -12x^{2}.

$$-12x^{2}-13x+4+11x-2$$

Combine -13x and 11x to get -2x.

$$-12x^{2}-2x+4-2$$

Subtract 2 from 4 to get 2.

$$-12x^{2}-2x+2$$

Expand

$$2-2x-12x^{2}$$

Solution Steps

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

$$3x^{2}-12x-x+4-\left(3x-1\right)\left(5x-2\right)$$

Combine -12x and -x to get -13x.

$$3x^{2}-13x+4-\left(3x-1\right)\left(5x-2\right)$$

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

$$3x^{2}-13x+4-\left(15x^{2}-6x-5x+2\right)$$

Combine -6x and -5x to get -11x.

$$3x^{2}-13x+4-\left(15x^{2}-11x+2\right)$$

To find the opposite of 15x^{2}-11x+2, find the opposite of each term.

$$3x^{2}-13x+4-15x^{2}-\left(-11x\right)-2$$

The opposite of -11x is 11x.

$$3x^{2}-13x+4-15x^{2}+11x-2$$

Combine 3x^{2} and -15x^{2} to get -12x^{2}.

$$-12x^{2}-13x+4+11x-2$$

Combine -13x and 11x to get -2x.

$$-12x^{2}-2x+4-2$$

Subtract 2 from 4 to get 2.

$$-12x^{2}-2x+2$$