Simplifying Polynomial Expressions
This article will guide you through the process of simplifying the following polynomial expression:
(a²b – 5ab + 2ab²) + (–4a²b + 3ab + 5ab²)
Understanding the Basics
Before we jump into the simplification, let's review a few key concepts:
 Polynomial: A polynomial is an expression consisting of variables and coefficients, combined using addition, subtraction, and multiplication.
 Like Terms: Like terms are terms that have the same variables raised to the same powers. For example, 3ab² and 2ab² are like terms, while 3ab² and 5ab are not.
 Combining Like Terms: To simplify polynomials, we combine like terms by adding or subtracting their coefficients.
Simplifying the Expression

Identify Like Terms:
 a²b terms: a²b and 4a²b
 ab terms: 5ab and 3ab
 ab² terms: 2ab² and 5ab²

Combine Like Terms:
 a²b terms: a²b  4a²b = 3a²b
 ab terms: 5ab + 3ab = 2ab
 ab² terms: 2ab² + 5ab² = 7ab²

Write the simplified expression:
The simplified expression is 3a²b  2ab + 7ab².
Conclusion
By identifying like terms and combining them, we have successfully simplified the given polynomial expression. This process is fundamental to understanding and manipulating algebraic expressions in various mathematical contexts.