The problem asks us to find the value of the mathematical expression: \( 2[3.5 \times 3.5 + 2.5 \times 2.5] \). To solve this, we need to follow the order of operations. First, we perform the calculations inside the square brackets. Within the brackets, we have multiplication and addition. According to the order of operations (BODMAS/PEMDAS), we perform multiplication before addition.

Steps to Calculate the Expression Value

Let's break down the calculation into simple steps:

1. Calculate the value of the first multiplication inside the brackets: \( 3.5 \times 3.5 \).
2. Calculate the value of the second multiplication inside the brackets: \( 2.5 \times 2.5 \).
3. Add the results obtained from steps 1 and 2. This gives us the total value inside the brackets.
4. Multiply the sum obtained in step 3 by 2, as indicated by the expression \( 2[\dots] \).

Performing the Calculations

Let's execute each step:

• Step 1: Calculate \( 3.5 \times 3.5 \).
  \( 3.5 \times 3.5 = 12.25 \)
• Step 2: Calculate \( 2.5 \times 2.5 \).
  \( 2.5 \times 2.5 = 6.25 \)
• Step 3: Add the results from Step 1 and Step 2.
  Sum inside brackets \( = 12.25 + 6.25 = 18.50 \)
• Step 4: Multiply the sum by 2.
  Expression value \( = 2 \times 18.50 = 37.00 \)

So, the value of the expression \( 2[3.5 \times 3.5 + 2.5 \times 2.5] \) is 37.

Verification of the Expression Value

We can double-check our calculation to ensure accuracy. The steps followed the standard order of operations, and the arithmetic was performed correctly.

The final calculated value is 37.

Revision Table: Expression Calculation Steps

Additional Information on Order of Operations

The order of operations is a set of rules that tells us the sequence in which to perform operations in a mathematical expression. A common acronym to remember this order is BODMAS or PEMDAS.

• BODMAS: Brackets, Orders (powers, roots), Division and Multiplication (from left to right), Addition and Subtraction (from left to right).
• PEMDAS: Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right).

In this problem, we first handled the operations inside the brackets, then performed the multiplications, followed by the addition within the brackets, and finally the multiplication outside the brackets. Understanding the order of operations is crucial for correctly evaluating mathematical expressions.