Which of the following pairs of expressions are equivalent?

Question

A)12⋅t+6 and 12(t+1/2)
B)−5(a−1) and −5⋅a−5
C)6(y+3) and 6⋅y+3
D)8⋅c+40 and 8(c−5)

Answer 1

A) 12⋅t+6 and 12(t+1/2) are equivalent because they simplify to the same expression.
12⋅t+6 simplifies to 12t+6.
12(t+1/2) simplifies to 12t+6.

B) −5(a−1) and −5⋅a−5 are equivalent because they simplify to the same expression.
−5(a−1) simplifies to −5a+5.
−5⋅a−5 does not simplify any further.

C) 6(y+3) and 6⋅y+3 are not equivalent.
6(y+3) simplifies to 6y+18.
6⋅y+3 does not simplify any further.

D) 8⋅c+40 and 8(c−5) are not equivalent.
8⋅c+40 does not simplify any further.
8(c−5) simplifies to 8c-40.

Therefore, the correct answer is A) 12⋅t+6 and 12(t+1/2)