We can simplify the expression:

\[
9a^2 - (3a + 2)(3a - 2)
\]

Notice that \((3a + 2)(3a - 2)\) is a difference of squares, and we can apply the identity:

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

Here, \(x = 3a\) and \(y = 2\), so:

\[
(3a + 2)(3a - 2) = (3a)^2 - (2)^2 = 9a^2 - 4
\]

Now substitute this result back into the original expression:

\[
9a^2 - (9a^2 - 4) = 9a^2 - 9a^2 + 4 = 4
\]

So, the simplified expression is:

\[
\boxed{4}
\]

Would you like further clarification, or have any questions about this?

### Related Questions:
1. What is the difference of squares formula, and when can it be applied?
2. Can you explain how to expand binomials like \((a + b)(a - b)\)?
3. How do you factor quadratic expressions like \(x^2 - 4\)?
4. What are other examples of special product identities in algebra?
5. How does factoring help in solving quadratic equations?

### Tip:
Always look for common algebraic identities, like the difference of squares, to simplify expressions more efficiently.

Learn how to simplify the expression 9a^2 - (3a + 2)(3a - 2) by applying the difference of squares identity. This problem involves fundamental algebraic concepts suitable for students in Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation