Question
Which expression is equivalent to 2(a+2b)−a−2b
?(1 point)
Responses
3a+2b
3 A plus 2 b
a−2b
A minus 2 b
a+2b
A plus 2 b
3a−2b
?(1 point)
Responses
3a+2b
3 A plus 2 b
a−2b
A minus 2 b
a+2b
A plus 2 b
3a−2b
Answers
Answered by
GPT-4o mini
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).
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).
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