Let's break down the expression step by step:

The expression is:

\[
84 + 2 \times \left(10 + \left(7 - 3\right)\right) - 3^2
\]

### Step 1: Solve the innermost parentheses
\[
7 - 3 = 4
\]
Now the expression becomes:
\[
84 + 2 \times \left(10 + 4\right) - 3^2
\]

### Step 2: Solve the next parentheses
\[
10 + 4 = 14
\]
Now the expression becomes:
\[
84 + 2 \times 14 - 3^2
\]

### Step 3: Handle the exponents
\[
3^2 = 9
\]
Now the expression becomes:
\[
84 + 2 \times 14 - 9
\]

### Step 4: Perform multiplication
\[
2 \times 14 = 28
\]
Now the expression becomes:
\[
84 + 28 - 9
\]

### Step 5: Perform the addition and subtraction from left to right
\[
84 + 28 = 112
\]
\[
112 - 9 = 103
\]

So, the final result is:

\[
\boxed{103}
\]

Would you like any more details or have any questions?

Here are some related questions:
1. What is the value of \(2(5 + (8 - 4)) - 4^2\)?
2. Can you simplify \(3(9 + (6 - 2)) - 5^3\)?
3. What does \(7^2 - 3(4 + (3 - 1)) + 2\) equal to?
4. How does changing the order of operations affect the result of \(50 + 3(8 + (7 - 5)) - 2^3\)?
5. Solve \(90 + 4(6 + (2 \times 3)) - 16\).

**Tip:** Always follow the order of operations (PEMDAS/BODMAS) to ensure correct results in mathematical expressions.

Understand how to solve the expression 84 + 2(10 + (7 - 3)) - 3^2 using the order of operations. This step-by-step guide covers arithmetic concepts, including parentheses, multiplication, and exponents. Suitable for students in Grades 5-7.

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