(a^2b–5ab+2ab^2)+(–4a^2b+3ab+5ab^2)

Jasonbradley

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Jun 16, 2024

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Simplifying Algebraic Expressions: (a^2b–5ab+2ab^2)+(–4a^2b+3ab+5ab^2)

This article will guide you through simplifying the algebraic expression: (a^2b–5ab+2ab^2)+(–4a^2b+3ab+5ab^2).

Understanding the Basics

Before we start simplifying, let's understand a few key points about algebraic expressions:

• Like Terms: Terms with the same variables raised to the same powers are considered like terms. For example, 3ab and -5ab are like terms, but 2ab^2 and 3ab are not.
• Combining Like Terms: We can add or subtract only like terms. When combining like terms, we simply add or subtract their coefficients.

Simplifying the Expression

1. Identify Like Terms:

   • a^2b: a^2b and -4a^2b are like terms.
   • ab: -5ab and 3ab are like terms.
   • ab^2: 2ab^2 and 5ab^2 are like terms.

2. Combine Like Terms:

   • a^2b: a^2b - 4a^2b = -3a^2b
   • ab: -5ab + 3ab = -2ab
   • ab^2: 2ab^2 + 5ab^2 = 7ab^2

3. Write the Simplified Expression: The simplified expression is -3a^2b - 2ab + 7ab^2.

Conclusion

By identifying like terms and combining them, we have successfully simplified the expression. The process of combining like terms is a fundamental concept in algebra and is essential for solving more complex algebraic equations and inequalities.