To factor the **difference of two squares**, we use the formula:

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

This formula states that any expression of the form \(a^2 - b^2\) can be factored into the product of two binomials: one with a sum and the other with a difference.

### Example:
Consider the expression \( x^2 - 9 \).

1. Identify \(a\) and \(b\):
   - Here, \(x^2\) is \(a^2\), so \(a = x\).
   - \(9\) is \(b^2\), so \(b = 3\).

2. Apply the formula:
   \[
   x^2 - 9 = (x + 3)(x - 3)
   \]

So, the factorization of \( x^2 - 9 \) is \( (x + 3)(x - 3) \).

### Another Example:
Factor the expression \( 16y^2 - 25z^2 \).

1. Identify \(a\) and \(b\):
   - \( 16y^2 \) is \( (4y)^2 \), so \(a = 4y\).
   - \( 25z^2 \) is \( (5z)^2 \), so \(b = 5z\).

2. Apply the formula:
   \[
   16y^2 - 25z^2 = (4y + 5z)(4y - 5z)
   \]

So, the factorization of \( 16y^2 - 25z^2 \) is \( (4y + 5z)(4y - 5z) \).

Do you want details or have any questions? Here are five questions for further exploration:

1. How can you recognize the difference of two squares in an algebraic expression?
2. Can the difference of two squares be used in simplifying complex algebraic fractions?
3. What happens if you attempt to factor the sum of two squares?
4. How is the difference of squares used in solving quadratic equations?
5. Can the difference of two squares formula be extended to higher powers?

**Tip:** Always check if an expression can be written in the form of \(a^2 - b^2\) before applying the difference of squares formula.

Learn how to factor the difference of two squares with detailed examples and explanations. Understand the difference of squares formula and its application in algebraic expressions. Suitable for high school students studying algebra.

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