The given expression is:

$A_n = (1 + 2)^2 - 1$

Let’s simplify this step by step.

1. First, calculate the sum inside the parentheses: $1 + 2 = 3$

2. Now, square the result: $3^2 = 9$

3. Finally, subtract 1: $9 - 1 = 8$

Thus, the simplified expression for $A_n$ is: $A_n = 8$

Would you like further details on this calculation or have any other questions?

Here are 5 related questions to explore further:

1. How would the result change if the sum inside the parentheses was $1 + n$ instead of $1 + 2$?
2. Can you find the value of $A_n$ if the equation was $A_n = (n + 2)^2 - 1$?
3. How does squaring a number affect its magnitude compared to just multiplying it by a factor?
4. What happens if the subtraction at the end was a different value, like $- 5$?
5. How could this equation be used to describe a sequence?

Tip: When simplifying expressions, always handle operations inside parentheses first, according to the order of operations (PEMDAS: Parentheses, Exponents, Multiplication and Division, Addition and Subtraction).