2-36b2.jpeg "(a-3b)2-36b2")
Simplifying the Expression: (a-3b)² - 36b²
This article will guide you through the process of simplifying the algebraic expression (a-3b)² - 36b². We'll use the principles of algebra and factorization to reach the most simplified form.
Step 1: Expanding the Square
The expression (a-3b)² represents the square of the binomial (a-3b). We can expand it using the formula:
(a - b)² = a² - 2ab + b²
Applying this formula to our expression:
(a - 3b)² = a² - 2(a)(3b) + (3b)²
Simplifying the multiplication:
(a - 3b)² = a² - 6ab + 9b²
Step 2: Substituting the Expanded Term
Now we can substitute the expanded term back into our original expression:
(a - 3b)² - 36b² = a² - 6ab + 9b² - 36b²
Step 3: Combining Like Terms
The terms 9b² and -36b² are like terms. Combining them:
a² - 6ab + 9b² - 36b² = a² - 6ab - 27b²
Final Result
Therefore, the simplified form of the expression (a-3b)² - 36b² is a² - 6ab - 27b².
Important Notes:
- Factoring: You can further factor the simplified expression. Notice that the expression now has a common factor of 3: 3(a² - 2ab - 9b²).
- Real-World Applications: This type of algebraic simplification is used in various fields, including physics, engineering, and finance. It helps to simplify complex equations and make them easier to work with.