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

Question

?(1 point)
Responses

3a+2b
3 A plus 2 b

a−2b
A minus 2 b

a+2b
A plus 2 b

3a−2b

Answer 1

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

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

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

3. Now, combine like terms:

   • For the \(a\) terms: \(2a - a = a\)
   • For the \(b\) terms: \(4b - 2b = 2b\)

4. Putting it all together gives us: \[ a + 2b \]

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

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