Let's break down the given expressions step by step.

Expression 1:

• Line 1: $2 \cdot (6 - 9)$

To simplify, we first calculate inside the parentheses: $6 - 9 = -3$ Now multiply: $2 \cdot (-3) = -6$

Thus, $2 \cdot (6 - 9) = -6$.

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Expression 2:

• Line 2: $2 \cdot 6 - 2 \cdot 9$

First, multiply each term: $2 \cdot 6 = 12$ $2 \cdot 9 = 18$ Now subtract: $12 - 18 = -6$

Thus, $2 \cdot 6 - 2 \cdot 9 = -6$.

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Answering the Fill-in-the-Blank Question:

1. "The expression was rewritten using the distributive property."
2. $2 \cdot (6 - 9) = 2 \cdot (-3)$ which equals -6.
3. $2 \cdot 6 - 2 \cdot 9 = 12 - 18$ which equals -6.

In conclusion, both expressions result in the same value, $-6$, showing the distributive property in action.

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Would you like more details on any part of this explanation?

Here are 5 relative questions to expand understanding:

1. What is the distributive property, and how is it used?
2. How does the order of operations affect solving equations?
3. Can you apply the distributive property to other expressions like $3 \cdot (4 + 5)$?
4. Why does $2 \cdot (6 - 9)$ equal $2 \cdot 6 - 2 \cdot 9$?
5. What happens if we change the numbers in the parentheses to $(9 - 6)$?

Tip: Always simplify the terms inside parentheses first before applying the distributive property!