(5x-3)-answer.jpeg "(5x+3)(5x-3) Answer")
Expanding (5x + 3)(5x - 3)
This expression is a classic example of the difference of squares pattern. Here's how to expand it:
Understanding the Difference of Squares
The difference of squares pattern states:
(a + b)(a - b) = a² - b²
This pattern arises because when you multiply the terms, the middle terms cancel each other out:
- a * a = a²
- a * -b = -ab
- b * a = ab
- b * -b = -b²
The -ab and ab terms cancel, leaving only a² - b².
Applying the Pattern
In our expression (5x + 3)(5x - 3):
- a = 5x
- b = 3
Applying the difference of squares pattern, we get:
(5x + 3)(5x - 3) = (5x)² - (3)²
Simplifying the Expression
Now, we simplify by squaring the terms:
(5x)² - (3)² = 25x² - 9
Conclusion
Therefore, the expanded form of (5x + 3)(5x - 3) is 25x² - 9. This demonstrates how recognizing patterns in algebra can simplify complex expressions.