To factorize \( 36 - x^2 \) using the difference of two squares method, we recognize that the difference of two squares formula is:

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

Here, \( 36 \) and \( x^2 \) are both perfect squares. Specifically:

- \( 36 = 6^2 \)
- \( x^2 = x^2 \)

Using the formula \( a^2 - b^2 \), we set \( a = 6 \) and \( b = x \). Substituting these into the formula, we get:

\[ 36 - x^2 = 6^2 - x^2 = (6 - x)(6 + x) \]

Therefore, the factorized form of \( 36 - x^2 \) is:

\[ 36 - x^2 = (6 - x)(6 + x) \]

Would you like further details or have any questions?

Here are 8 relative questions that expand on this topic:

1. What is the general form of the difference of two squares?
2. Can the difference of two squares be used to factorize \( 49 - y^2 \)?
3. How would you factorize \( 25 - 4x^2 \) using the difference of two squares?
4. What is the result of \( (a - b)(a + b) \) when expanded?
5. How do you identify perfect squares in algebraic expressions?
6. What are some other methods for factoring quadratic expressions?
7. How can the difference of two squares be applied in solving quadratic equations?
8. What are some practical applications of the difference of two squares in real-world problems?

**Tip:** When trying to factorize an expression, always check if it can be written in the form of a difference of two squares; this can simplify the process significantly.

Learn how to factorize the expression 36 - x² using the difference of two squares method. Understand the steps involved and practice problems related to this concept. Suitable for students in Grades 9-12.

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