https://file.aiquickdraw.com/mathbot/file/1726282367872hrtqc5mx.jpg

Let's solve both parts of the question one by one.

### Part (a) \((9x + \sqrt{2})(9x - \sqrt{2})\)

This is a difference of squares, which follows the formula:

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

Here, \(a = 9x\) and \(b = \sqrt{2}\).

Applying the formula:

\[
(9x + \sqrt{2})(9x - \sqrt{2}) = (9x)^2 - (\sqrt{2})^2
\]

Simplifying:

\[
= 81x^2 - 2
\]

So, the simplified expression for part (a) is:

\[
\boxed{81x^2 - 2}
\]

---

### Part (b) \((\sqrt{5}x - 2)(\sqrt{5}x + 2)\)

This is also a difference of squares, where \(a = \sqrt{5}x\) and \(b = 2\). Using the same formula:

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

Applying this:

\[
(\sqrt{5}x - 2)(\sqrt{5}x + 2) = (\sqrt{5}x)^2 - 2^2
\]

Simplifying:

\[
= 5x^2 - 4
\]

So, the simplified expression for part (b) is:

\[
\boxed{5x^2 - 4}
\]

---

If you have any questions or would like further details, feel free to ask!

### Follow-up Questions:
1. What is the difference of squares rule, and when is it applied?
2. Can you expand the binomials manually to verify the difference of squares?
3. How do you handle complex terms inside a difference of squares?
4. Can this method be applied to any pair of conjugates? Why?
5. What are some real-life applications of the difference of squares in algebra?

### Tip:
When simplifying expressions, always look for common patterns like the difference of squares or perfect square trinomials. This can save you time and reduce calculation errors.

Find each product. Simplify completely. a) (9x + √2)(9x - √2), b) (√5x - 2)(√5x + 2)

Learn how to simplify products using the difference of squares formula with detailed step-by-step solutions to (9x + √2)(9x - √2) and (√5x - 2)(√5x + 2). This problem covers key algebraic concepts for Grades 8-10.

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