(5x+3)^2-(5x-3)^2/x

Jasonbradley

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Jun 16, 2024

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Simplifying the Expression: (5x+3)^2 - (5x-3)^2 / x

This article will guide you through simplifying the given algebraic expression:

(5x+3)^2 - (5x-3)^2 / x

Understanding the Problem

The expression involves squaring binomials, subtraction, and division by a variable. We'll utilize the following key concepts:

• Difference of Squares: a² - b² = (a+b)(a-b)
• Simplifying Expressions: Combining like terms and canceling out common factors.

Step-by-Step Simplification

1. Expand the Squares:

   • (5x+3)² = (5x+3)(5x+3) = 25x² + 30x + 9
   • (5x-3)² = (5x-3)(5x-3) = 25x² - 30x + 9

2. Substitute into the Original Expression:

   • (25x² + 30x + 9) - (25x² - 30x + 9) / x

3. Simplify by Distributing the Negative Sign:

   • 25x² + 30x + 9 - 25x² + 30x - 9 / x

4. Combine Like Terms:

   • 60x / x

5. Cancel Common Factor:

   • 60

Final Result

The simplified expression is 60.

Key Takeaways

This problem demonstrates the power of algebraic manipulation and the importance of recognizing patterns like the difference of squares. By applying these principles, we can effectively simplify complex expressions and arrive at a concise and understandable solution.