(4ab-3c).jpeg "(4ab+3c)(4ab-3c)")
Factoring (4ab+3c)(4ab-3c)
This expression is a classic example of the difference of squares pattern. Here's how it works:
Understanding the Difference of Squares
The difference of squares pattern states:
(a + b)(a - b) = a² - b²
This pattern is extremely useful for factoring expressions quickly.
Applying the Pattern
Let's identify our 'a' and 'b' in the given expression:
- a = 4ab
- b = 3c
Now, substituting these values into the difference of squares formula:
(4ab + 3c)(4ab - 3c) = (4ab)² - (3c)²
Simplifying the Expression
Finally, we square both terms:
(4ab)² - (3c)² = 16a²b² - 9c²
Therefore, the factored form of (4ab+3c)(4ab-3c) is 16a²b² - 9c².