(5c-3d)^2-9d^2

Jasonbradley

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Jun 16, 2024

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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

1. 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

2. Combine terms with the monomial:

   • Now our expression is: 25c² - 30cd + 9d² - 9d²
   • The 9d² and -9d² terms cancel each other out.

3. 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.