Fill in the boxes in such a way that the multiplication process is simplified. Also, state the properties of multiplication used in the process.
`745 times 4 times 75 =745 times square=square`

Answer

To solve the problem, we need to fill in the boxes in the expression \( 745 \times 4 \times 75 = 745 \times \text{(blank)} = \text{(blank)} \).

### Step-by-Step Solution:

1. **Multiply 4 and 75**:
\[ 4 \times 75 = 300 \]
So, we can rewrite the expression as:
\[ 745 \times 4 \times 75 = 745 \times 300 \]

2. **Fill in the first blank**:
The first blank can be filled with \( 300 \) since \( 745 \times 4 \times 75 = 745 \times 300 \).

3. **Calculate the product \( 745 \times 300 \)**:
To find the product:
\[ 745 \times 300 \]
We can break it down as follows:
\[ 745 \times 300 = 745 \times (3 \times 100) = (745 \times 3) \times 100 \]
First, calculate \( 745 \times 3 \):
\[ 745 \times 3 = 2235 \]
Now, multiply by 100:
\[ 2235 \times 100 = 223500 \]

4. **Fill in the second blank**:
The second blank can be filled with \( 223500 \) since \( 745 \times 4 \times 75 = 745 \times 300 = 223500 \).

### Final Expression:
Thus, the complete expression is:
\[ 745 \times 4 \times 75 = 745 \times 300 = 223500 \]

### Properties of Multiplication Used:
1. **Associative Property of Multiplication**: This property states that when multiplying three or more numbers, the way in which the numbers are grouped does not change the product. Here, we grouped \( 4 \) and \( 75 \) together to simplify the multiplication.