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(4a^3-4a^2)+(6a^3+5a^2)

3 min read Jun 16, 2024
(4a^3-4a^2)+(6a^3+5a^2)

Simplifying Algebraic Expressions: (4a^3 - 4a^2) + (6a^3 + 5a^2)

This article will guide you through the process of simplifying the algebraic expression (4a^3 - 4a^2) + (6a^3 + 5a^2).

Understanding the Concepts

Before we dive into the simplification, let's recap some key concepts:

  • Terms: In an algebraic expression, terms are separated by addition or subtraction signs. For example, in the expression (4a^3 - 4a^2), "4a^3" and "-4a^2" are separate terms.
  • Like Terms: Like terms have the same variable(s) raised to the same power. For instance, 4a^3 and 6a^3 are like terms, while 4a^3 and 5a^2 are not.
  • Combining Like Terms: We can combine like terms by adding or subtracting their coefficients (the numerical part of a term).

Simplifying the Expression

  1. Identify like terms: In our expression (4a^3 - 4a^2) + (6a^3 + 5a^2), we can identify the following pairs of like terms:

    • 4a^3 and 6a^3
    • -4a^2 and 5a^2

  2. Combine like terms:

    • Combine the terms with 'a^3': 4a^3 + 6a^3 = 10a^3
    • Combine the terms with 'a^2': -4a^2 + 5a^2 = a^2

  3. Write the simplified expression: After combining the like terms, the simplified expression is 10a^3 + a^2.

Conclusion

Therefore, the simplified form of the expression (4a^3 - 4a^2) + (6a^3 + 5a^2) is 10a^3 + a^2. Remember, you can only combine terms that have the same variable and exponent.

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