Fill in the blanks and write the property used in each of the following.
`17 times (82-45)="______"-(17 times 45)`

Answer

To solve the problem, we need to fill in the blank in the equation:

\[ 17 \times (82 - 45) = "______" - (17 \times 45) \]

1. **Identify the property**: We will use the distributive property of multiplication over subtraction. The distributive property states that:

\[ a \times (b - c) = a \times b - a \times c \]

In our case, \( a = 17 \), \( b = 82 \), and \( c = 45 \).

2. **Apply the distributive property**: According to the distributive property, we can rewrite the left-hand side of the equation:

\[ 17 \times (82 - 45) = 17 \times 82 - 17 \times 45 \]

3. **Fill in the blank**: From the equation above, we can see that the left-hand side \( 17 \times (82 - 45) \) can be expressed as:

\[ 17 \times 82 - 17 \times 45 \]

Therefore, the blank can be filled with \( 17 \times 82 \).

4. **Final equation**: Now we can write the complete equation:

\[ 17 \times (82 - 45) = 17 \times 82 - (17 \times 45) \]

5. **Conclusion**: The filled blank is \( 17 \times 82 \), and the property used is the distributive property.

### Summary:
- The filled blank is: **17 times 82**
- The property used is: **Distributive Property of Multiplication over Subtraction**