Which of the following expressions is equivalent to 2a+4b+6c ?

Options

A. 8(a+b+c)
B. 2(a+2b)+3c)
C. 2(a+4b+6c)
D. 2(a+2b+3c)

Answer

To find an expression equivalent to \(2a + 4b + 6c\), we can factor out the common factor from the terms. Here’s a step-by-step solution:

### Step 1: Identify the common factor
The terms in the expression \(2a + 4b + 6c\) all have a common factor of 2.

### Step 2: Factor out the common factor
We can factor out 2 from each term:
\[ 2a + 4b + 6c = 2(a + 2b + 3c) \]

### Step 3: Write the factored expression
Now, we can express the original expression as:
\[ 2(a + 2b + 3c) \]

### Step 4: Check the options
Now we need to check which of the given options matches this expression. The options provided are:
- a) \(8a + b + c\)
- b) \(2a + 2b + 3c\)
- c) \(2a + 4b + 6c\)
- d) \(2a + 2b + 3c\)

### Step 5: Compare with the options
From our factored expression \(2(a + 2b + 3c)\), we can see that it is equivalent to \(2a + 4b + 6c\) but we need to check if any option matches \(a + 2b + 3c\).

None of the options directly match \(2(a + 2b + 3c)\) but we can see that option b) \(2a + 2b + 3c\) is incorrect since it does not match our expression.

### Conclusion
The expression \(2(a + 2b + 3c)\) does not match any of the options provided. The correct answer should be \(2(a + 2b + 3c)\), but since none of the options match, we conclude that the expression \(2a + 4b + 6c\) is already in its simplest form.