To expand and simplify the expression \((2 + \sqrt{3})(3 - \sqrt{3})\), we will use the distributive property (FOIL method) to multiply each term:

\[
(2 + \sqrt{3})(3 - \sqrt{3}) = 2(3) + 2(-\sqrt{3}) + \sqrt{3}(3) + \sqrt{3}(-\sqrt{3})
\]

Calculating each term:

1. \(2 \times 3 = 6\)
2. \(2 \times -\sqrt{3} = -2\sqrt{3}\)
3. \(\sqrt{3} \times 3 = 3\sqrt{3}\)
4. \(\sqrt{3} \times -\sqrt{3} = -3\)

Now, combine these results:

\[
6 - 2\sqrt{3} + 3\sqrt{3} - 3
\]

Combining like terms:

\[
(6 - 3) + (3\sqrt{3} - 2\sqrt{3}) = 3 + \sqrt{3}
\]

Therefore, the simplified form of \((2 + \sqrt{3})(3 - \sqrt{3})\) is:

\[
3 + \sqrt{3}
\]

Would you like to see more details or have any questions?

Here are 5 related questions to expand your understanding:

1. How would you expand and simplify \((2 - \sqrt{3})(3 + \sqrt{3})\)?
2. What is the result of \((1 + \sqrt{2})(1 - \sqrt{2})\)?
3. Can you simplify \((5 + \sqrt{7})(2 - \sqrt{7})\)?
4. What are the steps for multiplying binomials with different radical terms?
5. How can we factor an expression that involves radicals?

**Tip:** When dealing with radicals in expressions, try rationalizing the denominator or simplifying square roots whenever possible to get the simplest form.

expand and simplify (2 + root 3)(3 - root 3)

Learn how to expand and simplify the expression (2 + √3)(3 - √3) using the distributive property. This problem explores binomial expansion, radicals, and simplification techniques. Ideal for students in Grades 9-10, this guide breaks down the solution into easy-to-understand steps.

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