Fill in the boxes in such a way that the multiplication process is simplified. Also, state the properties of multiplication used in the process.
`539 times 22=539 times (20 +square)`

Answer

To solve the problem, we need to fill in the box in the expression \( 539 \times 22 = 539 \times (20 + \square) \) in a way that simplifies the multiplication.

### Step-by-Step Solution:

1. **Identify the numbers**: We have \( 22 \) which we can split into two parts: \( 20 \) and \( 2 \). This is because \( 20 + 2 = 22 \).

2. **Fill in the box**: We can write the expression as:
\[ 539 \times 22 = 539 \times (20 + 2) \]
Here, the box is filled with \( 2 \).

3. **Use the Distributive Property**: According to the Distributive Property of multiplication over addition, we can express the multiplication as:
\[ 539 \times (20 + 2) = 539 \times 20 + 539 \times 2 \]

4. **Final Expression**: Therefore, the complete equation is:
\[ 539 \times 22 = 539 \times 20 + 539 \times 2 \]

### Properties of Multiplication Used:
- **Distributive Property**: This property states that \( a \times (b + c) = a \times b + a \times c \). In this case, \( a = 539 \), \( b = 20 \), and \( c = 2 \).