To simplify the expression \(100a^4 - 81b^2\), we recognize that it is a difference of squares. Both \(100a^4\) and \(81b^2\) are perfect squares.

We rewrite the expression as:

\[ 100a^4 - 81b^2 = (10a^2)^2 - (9b)^2 \]

This fits the difference of squares formula:

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

Here, \(a = 10a^2\) and \(b = 9b\). Applying the formula, we get:

\[ (10a^2 - 9b)(10a^2 + 9b) \]

So, the simplified form of \(100a^4 - 81b^2\) is:

\[ (10a^2 - 9b)(10a^2 + 9b) \]

Would you like more details or have any questions?

Here are some related questions you might be interested in:
1. How do you factor trinomials?
2. What is the difference between prime and composite polynomials?
3. How do you factor polynomials by grouping?
4. What are some examples of perfect square trinomials?
5. How do you factor the sum or difference of cubes?
6. How can factoring help in solving polynomial equations?
7. What is synthetic division and when is it used?
8. How do you determine the roots of a polynomial equation?

**Tip:** Always check for a greatest common factor (GCF) first before applying other factoring techniques to simplify the process.

Learn how to simplify the expression 100a^4 - 81b^2 using the difference of squares formula with a detailed step-by-step solution. This problem covers algebraic manipulation techniques involving polynomials and the application of the difference of squares formula. Suitable for students in Grades 10-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation