Question

Which expressions are equivalent to
\[4b\] ?
Choose all answers that apply:
Choose all answers that apply:
(Choice A)
\[b+2(b+2b)\]
A
\[b+2(b+2b)\]
(Choice B)
\[3b+b\]
B
\[3b+b\]
(Choice C)
\[2(2b)\]
C
\[2(2b)\]

Answer 1

To determine which expressions are equivalent to \(4b\), let's simplify each of the choices given:

**Choice A: \(b + 2(b + 2b)\)**

First, simplify the expression inside the parentheses:
\[
b + 2b = 3b
\]

Now substitute that back:
\[
b + 2(3b) = b + 6b = 7b
\]
So, Choice A simplifies to \(7b\), which is not equivalent to \(4b\).

**Choice B: \(3b + b\)**

Now simplify this expression:
\[
3b + b = 4b
\]
So, Choice B is equivalent to \(4b\).

**Choice C: \(2(2b)\)**

Now simplify this expression:
\[
2(2b) = 4b
\]
So, Choice C is also equivalent to \(4b\).

Thus, the expressions that are equivalent to \(4b\) are:

- **Choice B:** \(3b + b\)
- **Choice C:** \(2(2b)\)

**Final Answer: B and C.**