Question

Which of the following pairs of expressions are equivalent?(1 point)
Responses

8⋅c+40
and 8(c−5)
8 times c plus 40 and 8 left parenthesis c minus 5 right parenthesis

6(y+3)
and 6⋅y+3
6 left parenthesis y plus 3 right parenthesis and 6 times y plus 3

12⋅t+6
and 12(t+12)
12 times t plus 6 and 12 left parenthesis t plus Start Fraction 1 over 2 End Fraction right parenthesis

−5(a−1)
and −5⋅a−5

Answer 1

To determine which pairs of expressions are equivalent, let's simplify or rewrite each expression.

1. **8⋅c + 40 and 8(c−5)**:
- 8(c - 5) = 8c - 40.
- So, 8c + 40 is not equal to 8(c - 5).
- **These expressions are not equivalent**.

2. **6(y + 3) and 6⋅y + 3**:
- 6(y + 3) = 6y + 18.
- So, 6(y + 3) is not equal to 6y + 3.
- **These expressions are not equivalent**.

3. **12⋅t + 6 and 12(t+12)**:
- 12(t + 12) = 12t + 144.
- So, 12t + 6 is not equal to 12(t + 12).
- **These expressions are not equivalent**.

4. **−5(a−1) and −5⋅a−5**:
- −5(a - 1) = -5a + 5.
- -5⋅a - 5 = -5a - 5.
- So, -5(a - 1) is not equal to -5⋅a - 5.
- **These expressions are not equivalent**.

**Final Conclusion**: None of the given pairs of expressions are equivalent.