Solve (6x+1)(1-2x)-(6x-1)(2x-1)

$$( 6 x + 1 ) ( 1 - 2 x ) - ( 6 x - 1 ) ( 2 x - 1 )$$

Evaluate

$$12x\left(1-2x\right)$$

Solution Steps

Apply the distributive property by multiplying each term of 6x+1 by each term of 1-2x.

$$6x-12x^{2}+1-2x-\left(6x-1\right)\left(2x-1\right)$$

Combine 6x and -2x to get 4x.

$$4x-12x^{2}+1-\left(6x-1\right)\left(2x-1\right)$$

Apply the distributive property by multiplying each term of 6x-1 by each term of 2x-1.

$$4x-12x^{2}+1-\left(12x^{2}-6x-2x+1\right)$$

Combine -6x and -2x to get -8x.

$$4x-12x^{2}+1-\left(12x^{2}-8x+1\right)$$

To find the opposite of 12x^{2}-8x+1, find the opposite of each term.

$$4x-12x^{2}+1-12x^{2}-\left(-8x\right)-1$$

The opposite of -8x is 8x.

$$4x-12x^{2}+1-12x^{2}+8x-1$$

Combine -12x^{2} and -12x^{2} to get -24x^{2}.

$$4x-24x^{2}+1+8x-1$$

Combine 4x and 8x to get 12x.

$$12x-24x^{2}+1-1$$

Subtract 1 from 1 to get 0.

$$12x-24x^{2}$$

Expand

$$12x-24x^{2}$$

Solution Steps

Apply the distributive property by multiplying each term of 6x+1 by each term of 1-2x.

$$6x-12x^{2}+1-2x-\left(6x-1\right)\left(2x-1\right)$$

Combine 6x and -2x to get 4x.

$$4x-12x^{2}+1-\left(6x-1\right)\left(2x-1\right)$$

Apply the distributive property by multiplying each term of 6x-1 by each term of 2x-1.

$$4x-12x^{2}+1-\left(12x^{2}-6x-2x+1\right)$$

Combine -6x and -2x to get -8x.

$$4x-12x^{2}+1-\left(12x^{2}-8x+1\right)$$

To find the opposite of 12x^{2}-8x+1, find the opposite of each term.

$$4x-12x^{2}+1-12x^{2}-\left(-8x\right)-1$$

The opposite of -8x is 8x.

$$4x-12x^{2}+1-12x^{2}+8x-1$$

Combine -12x^{2} and -12x^{2} to get -24x^{2}.

$$4x-24x^{2}+1+8x-1$$

Combine 4x and 8x to get 12x.

$$12x-24x^{2}+1-1$$

Subtract 1 from 1 to get 0.

$$12x-24x^{2}$$