2.jpeg "(3c−5)2")
Expanding (3c - 5)²
Expanding the expression (3c - 5)² involves applying the concept of squaring a binomial. This means multiplying the binomial by itself.
Here's how to expand it:
1. Understand the pattern:
The general pattern for squaring a binomial (a + b)² is:
(a + b)² = a² + 2ab + b²
2. Apply the pattern:
In our case, a = 3c and b = -5. Therefore:
(3c - 5)² = (3c)² + 2(3c)(-5) + (-5)²
3. Simplify the expression:
(3c)² + 2(3c)(-5) + (-5)² = 9c² - 30c + 25
Therefore, the expanded form of (3c - 5)² is 9c² - 30c + 25.
Key takeaways:
- Understanding the pattern for squaring a binomial is crucial for expanding these expressions.
- Be mindful of the signs when applying the pattern.
- Simplify the expression after applying the pattern to obtain the final result.