Let's simplify the expression step by step, using the order of operations (PEMDAS/BODMAS: Parentheses/Brackets, Exponents/Orders, Multiplication and Division (from left to right), Addition and Subtraction (from left to right)).
The expression is: \[ 12 - 8 \div 4 + [(6 + 2) - 3] \cdot 2 \cdot 3 \]
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Parentheses/Brackets:
- Simplify \( (6 + 2) \): \[ 6 + 2 = 8 \]
- Now the expression looks like: \[ 12 - 8 \div 4 + [8 - 3] \cdot 2 \cdot 3 \]
- Next, simplify \( [8 - 3] \): \[ 8 - 3 = 5 \]
- Now it becomes: \[ 12 - 8 \div 4 + 5 \cdot 2 \cdot 3 \]
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Exponents:
- There are no exponents to simplify.
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Multiplication and Division (from left to right):
- First, tackle \( 8 \div 4 \): \[ 8 \div 4 = 2 \]
- Now the expression becomes: \[ 12 - 2 + 5 \cdot 2 \cdot 3 \]
- Next, calculate \( 5 \cdot 2 \): \[ 5 \cdot 2 = 10 \]
- Multiply \( 10 \cdot 3 \): \[ 10 \cdot 3 = 30 \]
- Now the expression is: \[ 12 - 2 + 30 \]
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Addition and Subtraction (from left to right):
- First, perform \( 12 - 2 \): \[ 12 - 2 = 10 \]
- Then, add \( 10 + 30 \): \[ 10 + 30 = 40 \]
So, the simplified result of the expression is: \[ \boxed{40} \]