Solve left(x+2right)left(x-2x+4right)-xleft(x+2right)(x-2)

$$\left( x+2 \right) \left( x-2x+4 \right) -x \left( x+2 \right) (x-2)$$

Evaluate

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

Solution Steps

Combine x and -2x to get -x.

$$\left(x+2\right)\left(-x+4\right)-x\left(x+2\right)\left(x-2\right)$$

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

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

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

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

Use the distributive property to multiply x by x+2.

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

Apply the distributive property by multiplying each term of x^{2}+2x by each term of x-2.

$$-x^{2}+2x+8-\left(x^{3}-2x^{2}+2x^{2}-4x\right)$$

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

$$-x^{2}+2x+8-\left(x^{3}-4x\right)$$

To find the opposite of x^{3}-4x, find the opposite of each term.

$$-x^{2}+2x+8-x^{3}-\left(-4x\right)$$

The opposite of -4x is 4x.

$$-x^{2}+2x+8-x^{3}+4x$$

Combine 2x and 4x to get 6x.

$$-x^{2}+6x+8-x^{3}$$

Expand

$$8+6x-x^{2}-x^{3}$$

Solution Steps

Combine x and -2x to get -x.

$$\left(x+2\right)\left(-x+4\right)-x\left(x+2\right)\left(x-2\right)$$

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

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

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

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

Use the distributive property to multiply x by x+2.

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

Apply the distributive property by multiplying each term of x^{2}+2x by each term of x-2.

$$-x^{2}+2x+8-\left(x^{3}-2x^{2}+2x^{2}-4x\right)$$

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

$$-x^{2}+2x+8-\left(x^{3}-4x\right)$$

To find the opposite of x^{3}-4x, find the opposite of each term.

$$-x^{2}+2x+8-x^{3}-\left(-4x\right)$$

The opposite of -4x is 4x.

$$-x^{2}+2x+8-x^{3}+4x$$

Combine 2x and 4x to get 6x.

$$-x^{2}+6x+8-x^{3}$$