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

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

Evaluate

$$x^{4}-16$$

Solution Steps

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

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

Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}. Square 4.

$$\left(x^{2}\right)^{2}-16$$

To raise a power to another power, multiply the exponents. Multiply 2 and 2 to get 4.

$$x^{4}-16$$

Expand

$$x^{4}-16$$

Solution Steps

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

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

Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}. Square 4.

$$\left(x^{2}\right)^{2}-16$$

To raise a power to another power, multiply the exponents. Multiply 2 and 2 to get 4.

$$x^{4}-16$$