Certainly! Let's apply the distributive property to each of the expressions in detail.

### Detailed Step-by-Step Solutions Using the Distributive Property

1. **Expression:** \(-46 \times 999\)

   Using the distributive property:
   \[
   -46 \times 999 = -46 \times (1000 - 1)
   \]
   Distribute \(-46\):
   \[
   = (-46 \times 1000) + (-46 \times -1) = -46000 + 46 = -45954
   \]

2. **Expression:** \(-56 \times 35 + (-56) \times 15\)

   Notice that \(-56\) is a common factor:
   \[
   -56 \times 35 + (-56) \times 15 = -56(35 + 15)
   \]
   Add the numbers inside the parentheses:
   \[
   = -56 \times 50 = -2800
   \]

3. **Expression:** \(-63 \times -99\)

   Using the distributive property:
   \[
   -63 \times -99 = (-63) \times (-(100 - 1)) = -63 \times -100 + 63 \times 1
   \]
   Simplify each term:
   \[
   = 6300 + 63 = 6237
   \]

4. **Expression:** \(58 \times (-17) + (-58) \times 3\)

   Notice that \(58\) is a common factor with opposite signs:
   \[
   58 \times (-17) + (-58) \times 3 = 58 \times (-17) - 58 \times 3
   \]
   Factor out the common term:
   \[
   = 58(-17 - 3) = 58 \times -20 = -1160
   \]

### Final Distributed Property Solutions

1. \(-46 \times 999 = -45954\)
2. \(-56 \times 35 + (-56) \times 15 = -2800\)
3. \(-63 \times -99 = 6237\)
4. \(58 \times (-17) + (-58) \times 3 = -1160\)

Would you like more details or have any questions? Here are five more questions you might be interested in:

1. How do you solve linear equations?
2. What are the properties of exponents?
3. How do you find the derivative of a function?
4. What is the quadratic formula and how is it used?
5. How do you perform matrix multiplication?

**Tip:** Remember that the distributive property states \(a(b + c) = ab + ac\). This can simplify calculations and is particularly useful for mental math.

Explore detailed solutions applying the distributive property in mathematics. Learn how to simplify expressions using the distributive property with step-by-step examples. Suitable for Grades 6-8.

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