(2ab-5c).jpeg "(2ab+5c)(2ab-5c)")
Expanding the Expression (2ab + 5c)(2ab - 5c)
This expression is a classic example of the difference of squares pattern, which can be applied to simplify the multiplication.
Understanding the Difference of Squares
The difference of squares pattern states that:
(a + b)(a - b) = a² - b²
In our case, we can identify:
- a = 2ab
- b = 5c
Applying the Pattern
Using the difference of squares pattern, we can directly expand the expression:
(2ab + 5c)(2ab - 5c) = (2ab)² - (5c)²
Simplifying the Expression
Now, we just need to square each term:
(2ab)² - (5c)² = 4a²b² - 25c²
Final Result
Therefore, the expanded and simplified form of the expression (2ab + 5c)(2ab - 5c) is 4a²b² - 25c².
Key Takeaway
Recognizing and applying the difference of squares pattern is a powerful tool for simplifying algebraic expressions. By understanding the pattern, we can avoid the tedious task of expanding the expression manually and directly arrive at the simplified result.