The problem asks us to select the expressions that are equivalent to $8(5b)$.

1. Problem Description

The problem asks us to select the expressions that are equivalent to $8(5b)$.

2. Solution Steps

First, simplify the given expression $8(5b)$:

$8(5b) = 8 \cdot 5 \cdot b = 40b$

Now, let's analyze each option:

Option 1: $5b + 8$. This expression involves addition and cannot be simplified further. It is not equal to $40b$.

Option 2: $8(b \cdot 5)$. This can be rewritten as $8(5b) = 8 \cdot 5 \cdot b = 40b$. Therefore, this expression is equivalent to the original expression.

Option 3: $8(4b + b)$. We can simplify the expression within the parentheses first: $4b + b = 5b$. So, $8(4b + b) = 8(5b) = 8 \cdot 5 \cdot b = 40b$. Therefore, this expression is equivalent to the original expression.

Option 4: $8 + 5b$. This expression involves addition and cannot be simplified further. It is not equal to $40b$.

Therefore, only the second and third options are equivalent to $8(5b)$.

3. Final Answer

The expressions equivalent to $8(5b)$ are $8(b \cdot 5)$ and $8(4b + b)$.