Simplifying the Expression (5c  3d)²  9d²
This article will guide you through simplifying the algebraic expression (5c  3d)²  9d². We'll use the properties of exponents and the distributive property to arrive at a simplified form.
Understanding the Components
 (5c  3d)²: This represents the square of the binomial (5c  3d).
  9d²: This is a simple monomial term.
Simplifying the Expression

Expand the square:
 Recall that squaring a binomial means multiplying it by itself: (5c  3d)² = (5c  3d)(5c  3d)
 Use the FOIL (First, Outer, Inner, Last) method to expand the product:
 First: 5c * 5c = 25c²
 Outer: 5c * 3d = 15cd
 Inner: 3d * 5c = 15cd
 Last: 3d * 3d = 9d²
 Combine the like terms: 25c²  15cd  15cd + 9d² = 25c²  30cd + 9d²

Combine terms with the monomial:
 Now our expression is: 25c²  30cd + 9d²  9d²
 The 9d² and 9d² terms cancel each other out.

Final simplified expression:
 The simplified expression is 25c²  30cd.
Conclusion
By applying the distributive property and combining like terms, we successfully simplified the expression (5c  3d)²  9d² to 25c²  30cd. This process demonstrates how algebraic manipulations can lead to a more concise and manageable form of an expression.