Which expression is equivalent to 2(a+2b)−a−2b

Question

?(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)