(3x-5y)^2

2 min read Jun 16, 2024
(3x-5y)^2

Understanding (3x - 5y)²

In algebra, squaring a binomial like (3x - 5y)² means multiplying it by itself. This is a common operation encountered in various mathematical contexts. Here's a breakdown of how to expand and simplify this expression:

Expanding the Expression

To expand (3x - 5y)², we apply the distributive property (also known as FOIL method) which states that:

(a + b)² = a² + 2ab + b²

In our case:

  • a = 3x
  • b = -5y

Substituting these values into the formula:

(3x - 5y)² = (3x)² + 2(3x)(-5y) + (-5y)²

Simplifying the Expression

Now, we simplify each term:

  • (3x)² = 9x²
  • 2(3x)(-5y) = -30xy
  • (-5y)² = 25y²

Combining the simplified terms:

(3x - 5y)² = 9x² - 30xy + 25y²

Key Takeaways

  • Expanding binomials: The formula (a + b)² = a² + 2ab + b² is essential for expanding binomials.
  • Distributive Property: Understanding the distributive property is crucial for simplifying expressions.
  • Simplifying terms: Remember to simplify each term after expansion.

This simplified expression, 9x² - 30xy + 25y², represents the expanded form of (3x - 5y)². It's important to note that this expression cannot be simplified further.

Related Post


Featured Posts