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.