(2ab+3c)(2ab-3c)

Jasonbradley

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Jun 16, 2024

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Factoring the Expression (2ab + 3c)(2ab - 3c)

This expression is a classic example of the difference of squares pattern in algebra. Let's break down how to factor it:

Understanding the Difference of Squares

The difference of squares pattern states: a² - b² = (a + b)(a - b)

In our expression, we can identify the following:

• a = 2ab
• b = 3c

Applying the Pattern

1. Square the first term: (2ab)² = 4a²b²
2. Square the second term: (3c)² = 9c²
3. Subtract the squares: 4a²b² - 9c²

Now, we can rewrite our original expression using the difference of squares pattern:

(2ab + 3c)(2ab - 3c) = 4a²b² - 9c²

Conclusion

By recognizing the difference of squares pattern, we were able to easily factor the expression (2ab + 3c)(2ab - 3c) into 4a²b² - 9c². This demonstrates the power of pattern recognition in simplifying algebraic expressions.