To simplify the expression \((x + 8i)(x - 8i)\), we apply the difference of squares formula:

\[
(a + b)(a - b) = a^2 - b^2
\]

In this case:
- \( a = x \)
- \( b = 8i \)

Applying the formula:

\[
(x + 8i)(x - 8i) = x^2 - (8i)^2
\]

Now, simplify \( (8i)^2 \):
\[
(8i)^2 = 64i^2
\]

Since \( i^2 = -1 \), we get:

\[
64i^2 = 64(-1) = -64
\]

Thus, the expression simplifies to:

\[
x^2 - (-64) = x^2 + 64
\]

The final simplified expression is:

\[
x^2 + 64
\]

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Would you like more details or have any further questions?

Here are 5 related questions:
1. How do you simplify expressions with complex numbers?
2. Can you apply the difference of squares formula to any expression?
3. What happens when you square imaginary numbers?
4. What is the significance of \(i^2 = -1\)?
5. How do you handle complex conjugates in general?

**Tip:** When multiplying complex conjugates, the imaginary parts cancel out, leaving you with a real number result!

Learn how to simplify the expression (x + 8i)(x - 8i) by applying the difference of squares formula and the properties of imaginary numbers. This step-by-step guide is perfect for students in Grades 9-12, covering core algebraic and complex number concepts.

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