(3x2 + 5x + 7) - (-4x2 + 3x - 6)

Jasonbradley

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Jun 16, 2024

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Simplifying Polynomial Expressions: (3x² + 5x + 7) - (-4x² + 3x - 6)

This article will guide you through simplifying the polynomial expression: (3x² + 5x + 7) - (-4x² + 3x - 6).

Understanding the Concept

Before we begin, it's essential to understand that this expression involves subtracting two polynomials. To do this, we'll distribute the negative sign and then combine like terms.

Step-by-Step Solution

1. Distribute the negative sign:

   • The minus sign in front of the second polynomial changes the sign of each term inside the parentheses. This gives us:
   • (3x² + 5x + 7) + (4x² - 3x + 6)

2. Combine like terms:

   • x² terms: 3x² + 4x² = 7x²
   • x terms: 5x - 3x = 2x
   • Constant terms: 7 + 6 = 13

3. Write the simplified expression:

   • Combining the results from step 2, we get the simplified expression: 7x² + 2x + 13

Conclusion

Therefore, the simplified form of (3x² + 5x + 7) - (-4x² + 3x - 6) is 7x² + 2x + 13. Remember, the key to simplifying such expressions is to distribute the negative sign and then combine like terms.