(3a^2+1)-(4+2a^2)

Jasonbradley

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Jun 16, 2024

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Simplifying the Expression (3a² + 1) - (4 + 2a²)

This article will guide you through the process of simplifying the algebraic expression (3a² + 1) - (4 + 2a²).

Understanding the Problem

The expression involves parentheses, addition, and subtraction of terms with variables. We need to combine like terms to simplify it.

Step-by-Step Solution

1. Distribute the negative sign:

   • The negative sign before the second parentheses means we multiply each term inside the parentheses by -1: (3a² + 1) - (4 + 2a²) = 3a² + 1 - 4 - 2a²

2. Combine like terms:

   • Identify terms with the same variable and exponent: 3a² - 2a² + 1 - 4

3. Simplify:

   • Combine the 'a²' terms: (3 - 2)a² = a²
   • Combine the constant terms: 1 - 4 = -3

4. Final simplified expression:

   • a² - 3

Conclusion

Therefore, the simplified form of the expression (3a² + 1) - (4 + 2a²) is a² - 3. This process demonstrates the importance of understanding the order of operations and how to manipulate algebraic expressions effectively.