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To solve \( (x - 1)(x + 1) \), we can use the difference of squares formula, which states:

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

In this case, we have \( a = x \) and \( b = 1 \). Applying the formula:

\[
(x - 1)(x + 1) = x^2 - 1^2 = x^2 - 1
\]

Therefore, the correct answer is:

\[
x^2 - 1
\]

**Answer:** The first option, \( x^2 - 1 \), is correct.

Would you like further details on this topic, or do you have any questions?

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Here are five related questions to explore further:

1. What is the difference of squares, and how can it be applied in other problems?
2. How would you expand a binomial that is not a difference of squares, such as \( (x + 2)(x + 3) \)?
3. Can the difference of squares formula be used if both terms are negative, such as \( (-x - 1)(-x + 1) \)?
4. How does the distributive property relate to multiplying binomials like \( (x - 1)(x + 1) \)?
5. How would you factor \( x^2 - 1 \) back into binomial form?

**Tip:** Remember, the difference of squares is a quick way to simplify expressions involving two terms that are squares separated by a subtraction sign.

Explore how to multiply the expression (x - 1)(x + 1) by applying the difference of squares formula. This problem helps students understand key algebraic concepts in polynomial multiplication. Suitable for Grades 8-10.

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