Seth wrote the expression 5(y + 2) + 4 to show the amount of money five friends paid for snacks at a baseball game.

Which expression is equivalent to the one Seth wrote?

Select TWO answers.
A.5 + y + 5 + 2 + 4
B.5 · y · 5 · 2 + 4
C.5y + 10 + 4
D.5 · y · 4 + 5 · 2 · 4
E.5 · y + 5 · 2 + 4

Let's break down the expression Seth wrote and see which ones are equivalent:

Seth's expression is:  
\[
5(y + 2) + 4
\]

### Step-by-step simplification:

1. **Distribute the 5**:
   \[
   5(y + 2) = 5y + 10
   \]
   
2. **Add the 4**:
   \[
   5y + 10 + 4 = 5y + 14
   \]

### Now, let's check each option:

- **A. \( 5 + y + 5 + 2 + 4 \)**:
  - This is just adding all the terms separately without following order of operations. It doesn't simplify to \( 5y + 14 \). **Not equivalent**.

- **B. \( 5 \cdot y \cdot 5 \cdot 2 + 4 \)**:
  - This is incorrect because it involves multiplying \( 5 \), \( y \), \( 5 \), and \( 2 \) instead of distributing. **Not equivalent**.

- **C. \( 5y + 10 + 4 \)**:
  - This matches our simplified expression exactly. **Equivalent**.

- **D. \( 5 \cdot y \cdot 4 + 5 \cdot 2 \cdot 4 \)**:
  - This expression incorrectly multiplies \( 5y \) by \( 4 \) and multiplies \( 5 \times 2 \times 4 \). **Not equivalent**.

- **E. \( 5 \cdot y + 5 \cdot 2 + 4 \)**:
  - This correctly distributes \( 5 \) over \( y \) and \( 2 \), and then adds \( 4 \). It simplifies to \( 5y + 10 + 4 \), which equals \( 5y + 14 \). **Equivalent**.

### Correct answers:
- **C. 5y + 10 + 4**
- **E. 5 · y + 5 · 2 + 4**

Would you like more details or explanations?

### Related Questions:
1. How do you apply the distributive property in algebraic expressions?
2. What is the order of operations, and why is it important in simplifying expressions?
3. How can you check if two expressions are equivalent?
4. What is the difference between distributing and multiplying terms?
5. How do you simplify expressions involving parentheses and addition?

**Tip:** When simplifying expressions, always perform operations inside parentheses first before distributing!

Seth wrote the expression 5(y + 2) + 4 to show the amount of money five friends paid for snacks at a baseball game. Which expression is equivalent to the one Seth wrote? Select TWO answers. A.5 + y + 5 + 2 + 4 B.5 · y · 5 · 2 + 4 C.5y + 10 + 4 D.5 · y · 4 + 5 · 2 · 4 E.5 · y + 5 · 2 + 4

Discover how to simplify the algebraic expression 5(y + 2) + 4 using the distributive property. Learn which equivalent expressions match, and understand key algebraic principles such as distribution and the order of operations. Ideal for students in Grades 6-8.

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