(2x^2-4)-(-3x^2+2x-7)

Jasonbradley

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Jun 16, 2024

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Simplifying Expressions: (2x^2-4)-(-3x^2+2x-7)

In algebra, simplifying expressions involves combining like terms and performing operations to make the expression easier to understand and work with. Let's explore how to simplify the expression (2x^2-4)-(-3x^2+2x-7).

Understanding the Problem

The expression involves subtraction of two polynomials. The key to simplifying is to carefully distribute the negative sign and then combine like terms.

Step-by-Step Solution

1. Distribute the negative sign:

   • When we subtract a polynomial, we change the sign of each term inside the parentheses. This means: (2x^2-4) + (3x^2 - 2x + 7)

2. Combine like terms:

   • x^2 terms: 2x^2 + 3x^2 = 5x^2
   • x terms: -2x
   • Constant terms: -4 + 7 = 3

3. Write the simplified expression:

   • 5x^2 - 2x + 3

Conclusion

By following these steps, we have successfully simplified the expression (2x^2-4)-(-3x^2+2x-7) to 5x^2 - 2x + 3. Simplifying expressions is a fundamental skill in algebra, and understanding these principles allows for easier manipulation and solving of equations.