Let's solve the expression step by step:

\[
6 - 2 + 3 \times (2 - 3)^2
\]

### Step 1: Simplify inside the parentheses
\[
2 - 3 = -1
\]
So, the expression becomes:
\[
6 - 2 + 3 \times (-1)^2
\]

### Step 2: Square the value inside the parentheses
\[
(-1)^2 = 1
\]
Now the expression is:
\[
6 - 2 + 3 \times 1
\]

### Step 3: Multiply
\[
3 \times 1 = 3
\]
Now the expression becomes:
\[
6 - 2 + 3
\]

### Step 4: Add and subtract
\[
6 - 2 = 4
\]
\[
4 + 3 = 7
\]

So, the final answer is:
\[
\boxed{7}
\]

Do you want any further details or have any questions?

Here are 5 related questions to expand on this:

1. How do you simplify an expression with exponents like \((2 - 3)^2\)?
2. What is the order of operations (PEMDAS) and how does it work in solving problems like this?
3. Can you solve an expression with variables, such as \(6 - x + 3(x - 3)^2\)?
4. How do you handle negative numbers inside parentheses when raised to a power?
5. What happens when you multiply or divide terms with exponents of different signs?

**Tip:** Always follow the order of operations (PEMDAS: Parentheses, Exponents, Multiplication/Division, Addition/Subtraction) to simplify expressions correctly!

Step-by-step solution to the arithmetic problem 6 - 2 + 3 x (2 - 3)^2, demonstrating how to simplify expressions using the order of operations (PEMDAS). Learn how exponents and negative numbers work together in this calculation. Ideal for students in Grades 6-8.

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