## 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.