4(y + 8)Which expression is equivalent to the expression shown above?ResponsesA 4 + y + 4 + 84 +  y + 4 + 8B 4y + 84 y + 8C 4y + 324 y + 32D 4 + y + 8

1. ### Break Down the Problem

We need to simplify the expression $4(y + 8)$ and find which of the given responses is equivalent to it.

2. ### Relevant Concepts

The relevant concept here is the distributive property of multiplication over addition, which states that $a(b + c) = ab + ac$.

3. ### Analysis and Detail

Using the distributive property, we can simplify the expression $4(y + 8)$:

$4(y + 8) = 4y + 4 \cdot 8$

Calculating $4 \cdot 8$:

$4 \cdot 8 = 32$

Thus, we get:

$4(y + 8) = 4y + 32$

4. ### Verify and Summarize

Now we compare $4y + 32$ with the responses provided.

• Response A: $4 + y + 4 + 8 = y + 16$ (not equivalent)
• Response B: $4y + 8$ (not equivalent)
• Response C: $4y + 32$ (this matches)
• Response D: $4 + y + 8 = y + 12$ (not equivalent)

Final Answer

The equivalent expression is Response C: $4y + 32$.