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


Correct Answer: 1 point

Show Work: 1 point

(2 points)

2 answers

To simplify the expression \( 12 - 8 \div 4 + [(6 + 2) - 3] \cdot 2 \cdot 3 \), we will use the order of operations: parentheses, exponents, multiplication and division (from left to right), addition and subtraction (from left to right).

Let's break it down step by step.

  1. Calculate inside the parentheses: \[ 6 + 2 = 8 \] So, we now have: \[ 12 - 8 \div 4 + [8 - 3] \cdot 2 \cdot 3 \]

  2. Continue solving inside the brackets: \[ 8 - 3 = 5 \] Now the expression looks like: \[ 12 - 8 \div 4 + 5 \cdot 2 \cdot 3 \]

  3. Perform division: \[ 8 \div 4 = 2 \] Updating the expression gives us: \[ 12 - 2 + 5 \cdot 2 \cdot 3 \]

  4. Perform multiplication: \[ 5 \cdot 2 = 10 \] Continuing, we multiply: \[ 10 \cdot 3 = 30 \] Now, the expression simplifies to: \[ 12 - 2 + 30 \]

  5. Perform addition and subtraction from left to right: First, we do the subtraction: \[ 12 - 2 = 10 \] Then, we add: \[ 10 + 30 = 40 \]

Thus, the simplified result of the expression is: \[ \boxed{40} \]

Show Work Summary:

  1. Inside parentheses: \( (6 + 2) - 3 \) → \( 8 - 3 = 5 \)
  2. Division: \( 8 \div 4 = 2 \)
  3. Multiplication: \( 5 \cdot 2 = 10\), then \( 10 \cdot 3 = 30 \)
  4. Overall expression: \( 12 - 2 + 30 = 40 \)
shorter please :3