Expanding and Simplifying (a + 3b)^2  (a  3b)^2
This expression involves the difference of two squares, a common pattern in algebra. We can simplify it using the following steps:
Understanding the Difference of Squares Pattern
The difference of squares pattern states: a²  b² = (a + b)(a  b)
Applying the Pattern to our Expression

Identify a and b: In our expression, (a + 3b)²  (a  3b)², we can see that:
 a = (a + 3b)
 b = (a  3b)

Substitute into the pattern: Using the difference of squares pattern, we can rewrite the expression: [(a + 3b) + (a  3b)][(a + 3b)  (a  3b)]

Simplify:
 [(a + 3b) + (a  3b)] = 2a
 [(a + 3b)  (a  3b)] = 6b

Final Result: Therefore, (a + 3b)²  (a  3b)² simplifies to: 2a * 6b = 12ab
Conclusion
By recognizing and applying the difference of squares pattern, we were able to simplify the expression (a + 3b)²  (a  3b)² to 12ab. This demonstrates how understanding algebraic patterns can significantly simplify complex expressions.