(2x%2B3y-5).jpeg "(2x+3y+5)(2x+3y-5)")
Factoring the Expression (2x + 3y + 5)(2x + 3y - 5)
This expression represents a product of two binomials that share a common pattern. We can simplify this using the difference of squares pattern.
Understanding the Difference of Squares
The difference of squares pattern states that:
(a + b)(a - b) = a² - b²
Applying the Pattern
In our expression, we can consider:
- a = 2x + 3y
- b = 5
Therefore, applying the pattern:
(2x + 3y + 5)(2x + 3y - 5) = (2x + 3y)² - 5²
Simplifying the Expression
Now we can expand the squares:
(2x + 3y)² - 5² = (2x)² + 2(2x)(3y) + (3y)² - 25
Finally, we simplify:
4x² + 12xy + 9y² - 25
Conclusion
The factored expression (2x + 3y + 5)(2x + 3y - 5) simplifies to 4x² + 12xy + 9y² - 25. This process showcases the power of recognizing algebraic patterns to simplify complex expressions.