(3a2 + 2ab + 2b) + (5a2 − 3ab + 9)

Jasonbradley

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Jun 16, 2024

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Simplifying Algebraic Expressions: (3a² + 2ab + 2b) + (5a² − 3ab + 9)

This article will guide you through simplifying the algebraic expression: (3a² + 2ab + 2b) + (5a² − 3ab + 9).

Understanding the Basics

Before we start simplifying, let's understand the key concepts:

• Terms: Individual components of an algebraic expression separated by addition or subtraction signs. For example, in the expression (3a² + 2ab + 2b), there are three terms: 3a², 2ab, and 2b.
• Like Terms: Terms that have the same variables raised to the same powers. For example, 3a² and 5a² are like terms because they both have the variable 'a' raised to the power of 2.
• Combining Like Terms: This involves adding or subtracting coefficients of like terms. For instance, 3a² + 5a² = 8a².

Simplifying the Expression

1. Remove the parentheses: Since we are adding the expressions, the parentheses do not affect the order of operations. We can simply rewrite the expression as: 3a² + 2ab + 2b + 5a² − 3ab + 9

2. Identify like terms:

   • a² terms: 3a² and 5a²
   • ab terms: 2ab and -3ab
   • Constant terms: 2b and 9

3. Combine like terms:

   • 3a² + 5a² = 8a²
   • 2ab - 3ab = -ab
   • 2b + 9 = 2b + 9 (These are not like terms, so they remain separate)

4. Write the simplified expression: 8a² - ab + 2b + 9

Final Answer

The simplified form of the expression (3a² + 2ab + 2b) + (5a² − 3ab + 9) is 8a² - ab + 2b + 9.