Question

Using the distributive property, an expression equivalent to 34 + 16 is
2 (17 + 8).
17 (2 + 8).
34 + (4) (4).
(2) (17) + (4) (4).

Answer 1

To explore the expression equivalent to \(34 + 16\) using the distributive property, we start with the original expression itself:

\[
34 + 16
\]

Now let's evaluate the options provided:

1. **\(2(17 + 8)\)**
- This can be simplified as:
\[
2 \times 17 + 2 \times 8 = 34 + 16
\]
Therefore, this expression is equivalent to \(34 + 16\).

2. **\(17(2 + 8)\)**
- This can be simplified as:
\[
17 \times 2 + 17 \times 8 = 34 + 136
\]
Thus, this expression is not equivalent to \(34 + 16\).

3. **\(34 + (4)(4)\)**
- This evaluates to:
\[
34 + 16 \quad (\text{since } (4)(4) = 16)
\]
Therefore, this expression is equivalent to \(34 + 16\).

4. **\((2)(17) + (4)(4)\)**
- This simplifies to:
\[
34 + 16 \quad (\text{since } (2)(17) = 34 \text{ and } (4)(4) = 16)
\]
Therefore, this expression is also equivalent to \(34 + 16\).

Based on the evaluations, the expressions that are equivalent to \(34 + 16\) using the distributive property are:

- \(2(17 + 8)\)
- \(34 + (4)(4)\)
- \((2)(17) + (4)(4)\)

So, all three options 1, 3, and 4 are equivalent to \(34 + 16\).