(a2b–5ab+2ab2)+(–4a2b+3ab+5ab2)

Jasonbradley

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Jun 16, 2024

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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

1. Identify Like Terms:

   • a²b terms: a²b and -4a²b
   • ab terms: -5ab and 3ab
   • ab² terms: 2ab² and 5ab²

2. Combine Like Terms:

   • a²b terms: a²b - 4a²b = -3a²b
   • ab terms: -5ab + 3ab = -2ab
   • ab² terms: 2ab² + 5ab² = 7ab²

3. 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.