The given expression is \((9b - 1)(9b + 1)\). This is a difference of squares, which can be simplified using the formula:

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

In this case, \(a = 9b\) and \(b = 1\), so applying the formula:

\[
(9b - 1)(9b + 1) = (9b)^2 - 1^2
\]
\[
= 81b^2 - 1
\]

Thus, the simplified expression is:

\[
81b^2 - 1
\]

Would you like more details or have any questions?

Here are 5 related questions to expand this concept:
1. What is the general formula for factoring a difference of squares?
2. How would you simplify \((5x - 2)(5x + 2)\)?
3. Can all quadratic expressions be factored using the difference of squares method?
4. How do you factor an expression like \(100b^2 - 25\)?
5. What are some real-world applications of the difference of squares?

**Tip:** Whenever you see a pair of binomials with the same terms but opposite signs, check if the difference of squares formula can be applied!

Learn how to simplify the algebraic expression (9b-1)(9b+1) using the difference of squares formula. This solution breaks down the process step-by-step, making it easy for students in Grades 8-10 to understand and apply the concept to similar problems.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation