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

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

Evaluate

$$4x-1$$

Solution Steps

Use the distributive property to multiply 2x-1 by -3.

$$\left(-6x+3\right)x-\left(1-3x\right)\left(1+2x\right)$$

Use the distributive property to multiply -6x+3 by x.

$$-6x^{2}+3x-\left(1-3x\right)\left(1+2x\right)$$

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

$$-6x^{2}+3x-\left(1+2x-3x-6x^{2}\right)$$

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

$$-6x^{2}+3x-\left(1-x-6x^{2}\right)$$

To find the opposite of 1-x-6x^{2}, find the opposite of each term.

$$-6x^{2}+3x-1-\left(-x\right)-\left(-6x^{2}\right)$$

The opposite of -x is x.

$$-6x^{2}+3x-1+x-\left(-6x^{2}\right)$$

The opposite of -6x^{2} is 6x^{2}.

$$-6x^{2}+3x-1+x+6x^{2}$$

Combine 3x and x to get 4x.

$$-6x^{2}+4x-1+6x^{2}$$

Combine -6x^{2} and 6x^{2} to get 0.

$$4x-1$$

Expand

$$4x-1$$

Solution Steps

Use the distributive property to multiply 2x-1 by -3.

$$\left(-6x+3\right)x-\left(1-3x\right)\left(1+2x\right)$$

Use the distributive property to multiply -6x+3 by x.

$$-6x^{2}+3x-\left(1-3x\right)\left(1+2x\right)$$

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

$$-6x^{2}+3x-\left(1+2x-3x-6x^{2}\right)$$

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

$$-6x^{2}+3x-\left(1-x-6x^{2}\right)$$

To find the opposite of 1-x-6x^{2}, find the opposite of each term.

$$-6x^{2}+3x-1-\left(-x\right)-\left(-6x^{2}\right)$$

The opposite of -x is x.

$$-6x^{2}+3x-1+x-\left(-6x^{2}\right)$$

The opposite of -6x^{2} is 6x^{2}.

$$-6x^{2}+3x-1+x+6x^{2}$$

Combine 3x and x to get 4x.

$$-6x^{2}+4x-1+6x^{2}$$

Combine -6x^{2} and 6x^{2} to get 0.

$$4x-1$$