Solve (x-2)(x+4)-(2x+1)(1-x)

$$( x - 2 ) ( x + 4 ) - ( 2 x + 1 ) ( 1 - x )$$

Evaluate

$$3x^{2}+x-9$$

Solution Steps

Apply the distributive property by multiplying each term of x-2 by each term of x+4.

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

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

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

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

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

Combine 2x and -x to get x.

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

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

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

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

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

Combine 2x and -x to get x.

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

Combine x^{2} and 2x^{2} to get 3x^{2}.

$$3x^{2}+x-8-1$$

Subtract 1 from -8 to get -9.

$$3x^{2}+x-9$$

Expand

$$3x^{2}+x-9$$

Solution Steps

Apply the distributive property by multiplying each term of x-2 by each term of x+4.

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

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

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

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

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

Combine 2x and -x to get x.

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

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

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

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

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

Combine 2x and -x to get x.

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

Combine x^{2} and 2x^{2} to get 3x^{2}.

$$3x^{2}+x-8-1$$

Subtract 1 from -8 to get -9.

$$3x^{2}+x-9$$