Which pair of expressions are equivalent?
A.3+5a+−5
 and 3+a

B.2a+15(5a)
 and 2a+1

C.−18(−8a)
 and −a

D.3a+8a+(−8a)
 and 3a
what is the answer

Let's analyze each pair of expressions step by step to determine which are equivalent:

### A. \( 3 + 5a - 5 \) and \( 3 + a \)
Simplify the first expression:
\[
3 + 5a - 5 = (3 - 5) + 5a = -2 + 5a
\]
The second expression is \( 3 + a \).

These are not equivalent because \( -2 + 5a \neq 3 + a \).

---

### B. \( 2a + 15(5a) \) and \( 2a + 1 \)
Simplify the first expression:
\[
15(5a) = 75a
\]
So, \( 2a + 15(5a) = 2a + 75a = 77a \).

The second expression is \( 2a + 1 \).

These are not equivalent because \( 77a \neq 2a + 1 \).

---

### C. \( -18(-8a) \) and \( -a \)
Simplify the first expression:
\[
-18(-8a) = 144a
\]
The second expression is \( -a \).

These are not equivalent because \( 144a \neq -a \).

---

### D. \( 3a + 8a + (-8a) \) and \( 3a \)
Simplify the first expression:
\[
3a + 8a + (-8a) = 3a + (8a - 8a) = 3a + 0 = 3a
\]
The second expression is \( 3a \).

These **are** equivalent because \( 3a = 3a \).

---

### Conclusion:
The correct answer is **D. \( 3a + 8a + (-8a) \) and \( 3a \)**.

---

Do you want details or have any questions? Here are 5 related questions:

1. How do you simplify algebraic expressions with like terms?
2. What happens when you multiply negative numbers in algebra?
3. How can we factor an expression like \( 15(5a) \)?
4. What are the properties of equivalent expressions?
5. How do parentheses affect operations in expressions?

**Tip:** Always combine like terms when simplifying expressions to see equivalency.

Which pair of expressions are equivalent? A. 3 + 5a − 5 and 3 + a B. 2a + 15(5a) and 2a + 1 C. −18(−8a) and −a D. 3a + 8a + (−8a) and 3a what is the answer

Analyze which pair of algebraic expressions are equivalent. This problem involves simplifying expressions by combining like terms, using the distributive property, and working with negative numbers. Ideal for Grades 6-8 students learning basic algebra.

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