(3a^2-ab-2b^2)+(2a^2+5ab-3b^2)

Jasonbradley

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Jun 16, 2024

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Simplifying Algebraic Expressions: A Step-by-Step Guide

This article will guide you through the process of simplifying the algebraic expression (3a^2-ab-2b^2)+(2a^2+5ab-3b^2).

Understanding the Basics

Before we dive into the simplification process, let's understand a few key concepts:

• Algebraic Expressions: These are combinations of variables (like 'a' and 'b') and constants (like 3, -2, etc.) connected by mathematical operations like addition, subtraction, multiplication, and division.
• Like Terms: Terms with the same variables raised to the same power are called like terms. For example, 3a^2 and 2a^2 are like terms, but 3a^2 and -ab are not.

Simplifying the Expression

1. Identify like terms:

   • a^2 terms: 3a^2 and 2a^2
   • ab terms: -ab and 5ab
   • b^2 terms: -2b^2 and -3b^2

2. Combine like terms:

   • a^2 terms: 3a^2 + 2a^2 = 5a^2
   • ab terms: -ab + 5ab = 4ab
   • b^2 terms: -2b^2 - 3b^2 = -5b^2

3. Write the simplified expression: The simplified expression is 5a^2 + 4ab - 5b^2

Conclusion

By understanding the concepts of algebraic expressions and like terms, we can effectively simplify complex expressions. The process involves identifying like terms, combining them, and writing the simplified expression. Remember, practice is key to mastering simplification skills.