Consider the pair of expressions: A = 2(a + b) + 3b and B = 2a + 5b. Are A and B equivalent for all values of a and b? Provide justification.

No; A contains an extra b-term outside the parentheses, which makes it different from B for most values

Yes, but only when a and b are integers; otherwise, algebraic manipulation is invalid

Yes; after distributing the 2 and combining like terms, A simplifies to 2a + 5b, which equals B

They are equivalent only if b = 0, because only then does the outside 3b not affect the sum