Question

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

a−2b
A minus 2 b

a+2b
A plus 2 b

3a−2b
3 A minus 2 b

3a+2b
3 A plus 2 b

Answer 1

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

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

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

3. Next, combine like terms:
- For the \( a \) terms: \( 2a - a = a \)
- For the \( b \) terms: \( 4b - 2b = 2b \)

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

Thus, the expression \( 2(a + 2b) - a - 2b \) is equivalent to **\( a + 2b \)**.

The correct response is:
**a + 2b**
(A plus 2 b)