Answer the questions below about Line 1 and Line 2 shown below.
3, dot, left parenthesis, 5, minus, 2, right parenthesis
3⋅(5−2)
Line 1
3, dot, 5, minus, 3, dot, 2
3⋅5−3⋅2
Line 2
Answer
Attempt 1 out of 2

The expression was rewritten using the .
3, dot, left parenthesis, 5, minus, 2, right parenthesis3⋅(5−2) equals 3, dot3⋅  which equals .
3, dot, 5, minus, 3, dot, 23⋅5−3⋅2 equals  minus−  which equals .

In this case, we are asked to rewrite and solve the given mathematical expressions, focusing on understanding the steps taken in the process of simplifying the expressions. Here's how it works step-by-step:

### Line 1:
The original expression:
\[ 3 \cdot (5 - 2) \]

### Line 2:
The expression is rewritten using the **distributive property**, which allows us to distribute the multiplication over subtraction:
\[ 3 \cdot (5 - 2) = 3 \cdot 5 - 3 \cdot 2 \]

Now let's evaluate the result:

1. \( 3 \cdot 5 = 15 \)
2. \( 3 \cdot 2 = 6 \)

Thus:
\[ 15 - 6 = 9 \]

### Summary:
- The expression was rewritten using the **distributive property**.
- \( 3 \cdot (5 - 2) = 3 \cdot 5 - 3 \cdot 2 \), which equals \( 15 - 6 \), resulting in \( 9 \).

### Answering the blanks:
1. **Distributive property**.
2. \( 3 \cdot 5 - 3 \cdot 2 \).
3. \( 15 - 6 \).
4. \( 9 \).

Let me know if you'd like further details or if you have any questions.

Here are 5 related questions to expand your understanding:
1. What is the distributive property, and how is it applied to different operations?
2. Can you apply the distributive property to addition as well as subtraction?
3. How does the distributive property help simplify complex expressions?
4. What is the difference between the associative and distributive properties?
5. Can you use the distributive property in reverse to factor expressions?

**Tip:** Always look for opportunities to apply the distributive property when you see a multiplication outside of parentheses—it often simplifies calculations!

Learn how to simplify the expression 3⋅(5−2) using the distributive property. This detailed solution explains step-by-step how to rewrite the expression as 3⋅5−3⋅2 and evaluate it to get 9. Suitable for students in Grades 6-8.

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