%5E2.jpeg "(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.