The expression 6(b + c) is equivalent to 6b + 6c, by using the_______property.

Options

A. Commutative
B. Closure
C. Distributive
D. Identity

Answer

To solve the question, we need to identify the property that explains why the expression \(6(b + c)\) is equivalent to \(6b + 6c\).

### Step-by-Step Solution:

1. **Understanding the Expression**:
We start with the expression \(6(b + c)\). This means we are multiplying 6 by the sum of \(b\) and \(c\).

2. **Applying the Property**:
According to the distributive property, when you multiply a number by a sum, you can distribute the multiplication to each term inside the parentheses. So, we can rewrite \(6(b + c)\) as:
\[ 6(b + c) = 6 \cdot b + 6 \cdot c \]

3. **Simplifying the Expression**:
This simplifies to:
\[ 6b + 6c \]
Thus, we see that \(6(b + c)\) is indeed equivalent to \(6b + 6c\).

4. **Identifying the Property**:
The property that allows us to do this is called the **distributive property**.

5. **Final Answer**:
Therefore, we conclude that the expression \(6(b + c)\) is equivalent to \(6b + 6c\) by using the **distributive property**.