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The expanded and simplified form of the expression \((4 + \sqrt{2})(6 - \sqrt{2})\) is:

\[
22 + 2\sqrt{2}
\]

This is in the form \(b + c\sqrt{2}\), where:
- \(b = 22\)
- \(c = 2\)

Would you like any further explanation or have any questions?

Here are 5 related questions to expand your understanding:
1. How do we expand binomials using the distributive property?
2. What are conjugates, and how are they used in simplifying square root expressions?
3. How can you simplify expressions with surds (like \(\sqrt{2}\))?
4. What happens when multiplying two binomials containing irrational numbers?
5. Can you factor the resulting expression \(22 + 2\sqrt{2}\)?

**Tip:** When dealing with square roots, multiplying conjugates (\(a + \sqrt{b}\) and \(a - \sqrt{b}\)) results in a rational number.

Expand and simplify (4 + √2)(6 - √2). Give your answer in the form b + c√2.

Learn how to expand and simplify the expression (4 + √2)(6 - √2) using algebraic techniques like binomial expansion and the distributive property. This problem covers key algebraic concepts, including surds and properties of radicals. Suitable for students in Grades 9-11.

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