The expression \( 225p^2q^2 - 1 \) can be factored using the difference of squares formula. The difference of squares formula states that \( a^2 - b^2 = (a - b)(a + b) \).

First, we recognize that \( 225p^2q^2 \) is a perfect square, since:

\[ 225p^2q^2 = (15pq)^2 \]

Next, we write the expression as a difference of squares:

\[ 225p^2q^2 - 1 = (15pq)^2 - 1^2 \]

Using the difference of squares formula, we factor this expression:

\[ (15pq)^2 - 1^2 = (15pq - 1)(15pq + 1) \]

So, the factored form of \( 225p^2q^2 - 1 \) is:

\[ (15pq - 1)(15pq + 1) \]

Would you like further details or have any questions?

Here are 8 related questions to further explore this topic:

1. How do you factor other expressions using the difference of squares formula?
2. What is the general form of the difference of squares?
3. Can you explain the process of identifying perfect squares in an expression?
4. How do you recognize when to use the difference of squares in factoring?
5. What are other examples of factoring differences of squares?
6. How can the difference of squares be applied in solving quadratic equations?
7. Are there other special factoring formulas similar to the difference of squares?
8. How does factoring help in simplifying algebraic expressions?

**Tip:** Always look for common factors first before applying special factoring formulas.

Learn how to factor the expression 225p²q² - 1 using the difference of squares formula. This problem covers key algebraic concepts, including the difference of squares formula and its application in factoring quadratic expressions. Suitable for high school students in Grades 10-12.

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