If `- 3a + 2b + 5c` is subtracted from `2a + b - 8c,` what will be the result ?

Options

A. `5a - b + 13 c`
B. `a + b - 13 c`
C. `5a + b + 13 c`
D. `5a - b - 13 c`

Answer

To solve the problem, we need to subtract the expression `-3a + 2b + 5c` from the expression `2a + b - 8c`. This can be represented mathematically as:

\[ (2a + b - 8c) - (-3a + 2b + 5c) \]

### Step 1: Rewrite the expression
We can rewrite the subtraction of the second expression as adding its opposite:

\[ 2a + b - 8c + 3a - 2b - 5c \]

### Step 2: Combine like terms
Now, we will combine the like terms (the terms with `a`, `b`, and `c`):

- For the `a` terms:
\[ 2a + 3a = 5a \]

- For the `b` terms:
\[ b - 2b = -b \]

- For the `c` terms:
\[ -8c - 5c = -13c \]

### Step 3: Write the final result
Now, we can combine all the results from the previous step:

\[ 5a - b - 13c \]

Thus, the result of subtracting `-3a + 2b + 5c` from `2a + b - 8c` is:

\[ \boxed{5a - b - 13c} \]