Let's evaluate the expression \( 3\left(4 - 7\right)^2 \) step by step.

### Step 1: Simplify inside the parentheses.
First, calculate \( 4 - 7 \):
\[
4 - 7 = -3
\]
So the expression becomes:
\[
3(-3)^2
\]

### Step 2: Square the result.
Now, square \(-3\):
\[
(-3)^2 = 9
\]
So the expression simplifies to:
\[
3 \times 9
\]

### Step 3: Multiply by 3.
Finally, multiply \( 9 \) by \( 3 \):
\[
3 \times 9 = 27
\]

### Final Answer:
\[
3(4 - 7)^2 = 27
\]

Would you like any more details or have any questions? Here are some related questions you might find interesting:

1. What happens when you square a negative number?
2. How would the expression change if we used addition instead of subtraction inside the parentheses?
3. What role does the coefficient (in this case, 3) play in the expression?
4. How does the order of operations affect the final result?
5. What if the value inside the parentheses was a fraction instead of an integer?

**Tip:** Always simplify the expression inside the parentheses first before applying other operations like squaring or multiplying.

Learn how to evaluate the expression 3(4 - 7)^2 with a detailed step-by-step solution. This problem covers key arithmetic concepts, including simplifying expressions with exponents. Suitable for students in Grades 6-8.

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