## Solving the Equation: (x^2 + 8)(x^2 - 8) = 0

This equation presents a straightforward approach to solving for the unknown variable 'x'. The key lies in understanding the **Zero Product Property**. This property states that if the product of two or more factors is zero, then at least one of the factors must be zero.

Let's apply this to our equation:

**(x^2 + 8)(x^2 - 8) = 0**

We have two factors: **(x^2 + 8)** and **(x^2 - 8)**. To make the product equal to zero, at least one of these factors must be equal to zero.

Therefore, we set each factor equal to zero and solve:

**1. x^2 + 8 = 0**

- Subtract 8 from both sides:
- x^2 = -8

- Take the square root of both sides:
- x = ±√(-8)

- Simplify:
- x = ±2√(-2)

- Express in terms of imaginary unit 'i' (where i² = -1):
**x = ±2i√2**

**2. x^2 - 8 = 0**

- Add 8 to both sides:
- x^2 = 8

- Take the square root of both sides:
- x = ±√8

- Simplify:
**x = ±2√2**

Therefore, the solutions to the equation (x^2 + 8)(x^2 - 8) = 0 are:

**x = 2√2****x = -2√2****x = 2i√2****x = -2i√2**