find the simplified value of [2+4x5{10-4x2}]

Options

A. 40
B. 42
C. 44
D. 46

Explanation

To find the simplified value of the expression \(2 + 4 \times 5 \{10 - 4 \times 2\}\), 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)).

### Step-by-Step Solution:

1. **Identify the expression**:
\[ 2 + 4 \times 5 \{10 - 4 \times 2\} \]

2. **Calculate inside the braces first**:
- We need to solve \(10 - 4 \times 2\).
- According to the order of operations, we first perform the multiplication:
\[ 4 \times 2 = 8 \]
- Now substitute back into the expression:
\[ 10 - 8 = 2 \]

3. **Substitute back into the expression**:
- Now the expression becomes:
\[ 2 + 4 \times 5 \times 2 \]

4. **Calculate the multiplication**:
- First, calculate \(4 \times 5\):
\[ 4 \times 5 = 20 \]
- Now substitute back:
\[ 2 + 20 \times 2 \]
- Now calculate \(20 \times 2\):
\[ 20 \times 2 = 40 \]

5. **Add the results**:
- Now add \(2 + 40\):
\[ 2 + 40 = 42 \]

### Final Answer:
The simplified value of the expression is \(42\).

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