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To solve the equation \( 4(10 + 5) = 6(12 - 2) \) using the distributive property, let's break it down step by step.

### Left Side: \( 4(10 + 5) \)
Using the distributive property, distribute the \( 4 \) to both terms inside the parentheses:
\[
4(10) + 4(5) = 40 + 20
\]
So, the left-hand side becomes \( 40 + 20 \).

### Right Side: \( 6(12 - 2) \)
Similarly, distribute the \( 6 \) to both terms inside the parentheses:
\[
6(12) - 6(2) = 72 - 12
\]
So, the right-hand side becomes \( 72 - 12 \).

### Final Equation:
Putting both sides together, the equation becomes:
\[
40 + 20 = 72 - 12
\]

This matches the first option in the list.

**Answer**: The correct answer is \( \boxed{40 + 20 = 72 - 12} \).

Would you like further details or have any other questions?

Here are 5 related questions to expand on this concept:
1. How would you apply the distributive property to the equation \( 3(x + 7) = 21 \)?
2. What is the reverse of applying the distributive property called?
3. How does the distributive property work with subtraction inside parentheses?
4. Can the distributive property be used with more than two terms inside the parentheses?
5. How do you solve an equation after distributing both sides?

**Tip**: The distributive property can help simplify equations, especially when working with variables or larger numbers. Always distribute multiplication to each term within the parentheses.

How could you correctly rewrite the equation 4(10 + 5) = 6(12 - 2) using the distributive property?

Learn how to correctly rewrite the equation 4(10 + 5) = 6(12 - 2) using the distributive property. This problem demonstrates key algebraic concepts and how the distributive property applies to equations. Suitable for Grades 6-8.

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