Question

Use the order of operations to simplify the following expression: 12−8÷4+[(6+2)−3]^2 x3

Correct Answer: 1 point

Show Work: 1 point

(2 points)

Answer 1

To simplify the expression \( 12 - 8 \div 4 + [(6 + 2) - 3]^2 \times 3 \), we will follow the order of operations, often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right)).

1. **Evaluate inside the brackets**:
\[
(6 + 2) - 3 = 8 - 3 = 5
\]
So we can substitute \(5\) back into the expression:
\[
12 - 8 \div 4 + [5]^2 \times 3
\]

2. **Calculate the exponent**:
\[
[5]^2 = 25
\]
Now the expression looks like:
\[
12 - 8 \div 4 + 25 \times 3
\]

3. **Perform the division**:
\[
8 \div 4 = 2
\]
The expression now is:
\[
12 - 2 + 25 \times 3
\]

4. **Perform the multiplication**:
\[
25 \times 3 = 75
\]
Now the expression is:
\[
12 - 2 + 75
\]

5. **Now perform the addition and subtraction from left to right**:
- First, calculate \(12 - 2\):
\[
12 - 2 = 10
\]
- Next, add \(10 + 75\):
\[
10 + 75 = 85
\]

So the final simplified value of the expression is \(\boxed{85}\).

**Show Work Summary**:
1. Simplified the bracket: \( (6 + 2) - 3 = 5 \)
2. Squared the result: \( [5]^2 = 25 \)
3. Performed the division: \( 8 \div 4 = 2 \)
4. Multiplied the square: \( 25 \times 3 = 75 \)
5. Processed the result by order: \( 12 - 2 + 75 = 85 \)

Final answer: \( 85 \)