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The question asks you to use the distributive property to simplify the expression \( 10(5r - 5s + 7) \).

### Applying the distributive property:
The distributive property states that \( a(b + c) = ab + ac \), meaning we multiply each term inside the parentheses by the factor outside the parentheses (in this case, 10).

Let's distribute:

\[
10(5r - 5s + 7) = (10 \times 5r) + (10 \times -5s) + (10 \times 7)
\]

Now simplify each term:

\[
10 \times 5r = 50r
\]
\[
10 \times -5s = -50s
\]
\[
10 \times 7 = 70
\]

### Final simplified expression:
\[
50r - 50s + 70
\]

This is the equivalent expression after applying the distributive property.

Would you like further clarification or have any questions?

Here are 5 related questions to further practice:
1. What is the distributive property in reverse (factoring)?
2. Can you apply the distributive property to \( 7(2x + 4y - 3) \)?
3. How would the expression change if the coefficient outside the parentheses was negative?
4. How would the distributive property be used in an equation like \( 3(x - 2) = 12 \)?
5. What happens if the expression inside the parentheses has more than 3 terms?

**Tip:** When applying the distributive property, make sure to distribute to each term inside the parentheses, keeping track of signs (positive or negative).

Use the distributive property to write an equivalent expression: 10(5r - 5s + 7).

Learn how to apply the distributive property to simplify the expression 10(5r - 5s + 7). This problem is ideal for students in Grades 6-8 studying algebra and the distributive property of multiplication over addition and subtraction.

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