Simplifying the Expression: (5x+3)^2  (5x3)^2 / x
This article will guide you through simplifying the given algebraic expression:
(5x+3)^2  (5x3)^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)(ab)
 Simplifying Expressions: Combining like terms and canceling out common factors.
StepbyStep Simplification

Expand the Squares:
 (5x+3)² = (5x+3)(5x+3) = 25x² + 30x + 9
 (5x3)² = (5x3)(5x3) = 25x²  30x + 9

Substitute into the Original Expression:
 (25x² + 30x + 9)  (25x²  30x + 9) / x

Simplify by Distributing the Negative Sign:
 25x² + 30x + 9  25x² + 30x  9 / x

Combine Like Terms:
 60x / x

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.