Add :
`3b - 7c + 10, 5c - 2b - 15, 15 + 12c + b`

Answer

To add the algebraic expressions \(3b - 7c + 10\), \(5c - 2b - 15\), and \(15 + 12c + b\), we will follow these steps:

### Step 1: Write down the expressions
We have the following expressions:
1. \(3b - 7c + 10\)
2. \(5c - 2b - 15\)
3. \(15 + 12c + b\)

### Step 2: Group like terms
We will group the terms based on their variables:
- Terms with \(b\): \(3b\), \(-2b\), and \(b\)
- Terms with \(c\): \(-7c\), \(5c\), and \(12c\)
- Constant terms: \(10\), \(-15\), and \(15\)

### Step 3: Add the \(b\) terms
Now, we will add the \(b\) terms together:
\[ 3b - 2b + b = (3 - 2 + 1)b = 2b \]

### Step 4: Add the \(c\) terms
Next, we will add the \(c\) terms together:
\[ -7c + 5c + 12c = (-7 + 5 + 12)c = 10c \]

### Step 5: Add the constant terms
Now, we will add the constant terms together:
\[ 10 - 15 + 15 = (10 - 15 + 15) = 10 \]

### Step 6: Combine all the results
Now we can combine all the results from the previous steps:
\[ 2b + 10c + 10 \]

### Final Answer
Thus, the sum of the given expressions is:
\[ 2b + 10c + 10 \]

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