Question

Which of the following pairs of expressions are equivalent?
A. 8 * c + 40 and 8 (c - 5)
B. 12 * t + 6 and 12 (t + 1/3)
C. 6(y + 3) and 6 * y + 3
D. -5 (a - 1) and -5 * a -5

Answer 1

To check if the pairs of expressions are equivalent, we'll simplify each expression and compare them.

**A.** \( 8c + 40 \) and \( 8(c - 5) \)

Simplifying the second expression:
\[
8(c - 5) = 8c - 40
\]
So, we have:
- \( 8c + 40 \)
- \( 8c - 40 \)

These are not equivalent.

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**B.** \( 12t + 6 \) and \( 12(t + \frac{1}{3}) \)

Simplifying the second expression:
\[
12(t + \frac{1}{3}) = 12t + 4
\]
So, we have:
- \( 12t + 6 \)
- \( 12t + 4 \)

These are not equivalent.

---

**C.** \( 6(y + 3) \) and \( 6y + 3 \)

Simplifying the first expression:
\[
6(y + 3) = 6y + 18
\]
So, we have:
- \( 6y + 18 \)
- \( 6y + 3 \)

These are not equivalent.

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**D.** \( -5(a - 1) \) and \( -5a - 5 \)

Simplifying the first expression:
\[
-5(a - 1) = -5a + 5
\]
So, we have:
- \( -5a + 5 \)
- \( -5a - 5 \)

These are not equivalent.

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In conclusion, none of the pairs of expressions are equivalent.