Question

Which expression is equivalent to 2(a+2b)−a−2b
?(1 point)
Responses

a−2b
A minus 2 b

3a−2b
3 A minus 2 b

3a+2b
3 A plus 2 b

a+2b

Answer 1

To simplify the expression \( 2(a + 2b) - a - 2b \), we can follow these steps:

1. Distribute the \( 2 \) in the first term:
\[
2(a + 2b) = 2a + 4b
\]

2. Substitute this back into the expression:
\[
2a + 4b - a - 2b
\]

3. Combine like terms:
- Combine \( 2a - a \):
\[
2a - a = a
\]
- Combine \( 4b - 2b \):
\[
4b - 2b = 2b
\]

Putting it all together, we have:
\[
a + 2b
\]

So, the expression \( 2(a + 2b) - a - 2b \) simplifies to \( a + 2b \).

Therefore, the correct response is:
**\( a + 2b \)**