https://file.aiquickdraw.com/mathbot/file/1728757671299a4kctufu.jpg

To solve the given expression:

\[
(1 - \sqrt{3})(\sqrt{3} + 1)
\]

we can use the distributive property (FOIL method), which states that:

\[
(a - b)(c + d) = ac + ad - bc - bd
\]

Applying this to the expression:

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

Adding these results together gives:

\[
\sqrt{3} + 1 - 3 - \sqrt{3} = 1 - 3 = -2
\]

So, the simplified result of the expression is:

\[
-2
\]

Would you like more details or have any questions?

### Related Questions:
1. How does the distributive property work with expressions containing square roots?
2. Can you explain how to simplify expressions with radicals further?
3. What are the steps to solve more complex radical expressions?
4. How does this process change if there are more terms in the expression?
5. How can the result be verified using another method?

### Tip:
When working with radicals, remember that \(\sqrt{a} \cdot \sqrt{a} = a\), which can help simplify the expressions quickly.

Solve and simplify the radical expression (1 - √3)(√3 + 1) using the distributive property. This problem demonstrates key algebraic principles and radical simplification techniques, suitable for students in Grades 8-10.

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