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

$$(x+2)( { x }^{ 2 } -2x+4)-(x-2)( { x }^{ 2 } +2x+4)$$

Evaluate

$$16$$

Solution Steps

Use the distributive property to multiply x+2 by x^{2}-2x+4 and combine like terms.

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

Use the distributive property to multiply x-2 by x^{2}+2x+4 and combine like terms.

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

To find the opposite of x^{3}-8, find the opposite of each term.

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

Combine x^{3} and -x^{3} to get 0.

$$8+8$$

Add 8 and 8 to get 16.

$$16$$

Factor

$$2^{4}$$