Question

Which of the following pairs of expression are equivalent A 8 • C + 40 and 8 ( c - 5 ) B 12 • t + 6 and 12 ( t + 1/2 ) C -5 ( a - 1 ) and -5 • a - 5 D 6 ( y + 3 ) and 6 • y + 3

Answer 1

To determine if the given pairs of expressions are equivalent, we can simplify each expression and see if they result in the same value.

Let's analyze each pair:

**A)** \( 8 \cdot C + 40 \) and \( 8 (C - 5) \)

1. Expand \( 8 (C - 5) \):
\[
8 (C - 5) = 8C - 40
\]

Comparing \( 8C + 40 \) with \( 8C - 40 \), they are not equivalent.

**B)** \( 12 \cdot t + 6 \) and \( 12 (t + 1/2) \)

1. Expand \( 12 (t + 1/2) \):
\[
12 (t + 1/2) = 12t + 6
\]

Since both \( 12t + 6 \) are the same, these expressions are equivalent.

**C)** \( -5 (a - 1) \) and \( -5 \cdot a - 5 \)

1. Expand \( -5 (a - 1) \):
\[
-5 (a - 1) = -5a + 5
\]

Comparing \( -5a + 5 \) with \( -5a - 5 \), they are not equivalent.

**D)** \( 6 (y + 3) \) and \( 6 \cdot y + 3 \)

1. Expand \( 6 (y + 3) \):
\[
6 (y + 3) = 6y + 18
\]

Comparing \( 6 (y + 3) \) with \( 6y + 3 \), they are not equivalent.

Thus, the only equivalent pair is:

**B)** \( 12 \cdot t + 6 \) and \( 12 (t + 1/2) \).