Add : `3ax+5by -cz, by-6ax-3cz and 5cz-ax-2by`.

Answer

To solve the problem of adding the algebraic expressions \(3ax + 5by - cz\), \(by - 6ax - 3cz\), and \(5cz - ax - 2by\), we will follow these steps:

### Step 1: Write down the expressions
We have three expressions to add:
1. \(3ax + 5by - cz\)
2. \(by - 6ax - 3cz\)
3. \(5cz - ax - 2by\)

### Step 2: Combine like terms
To add these expressions, we will group the like terms together. The like terms are those that have the same variable part.

- For \(ax\) terms: \(3ax\), \(-6ax\), and \(-ax\)
- For \(by\) terms: \(5by\), \(by\), and \(-2by\)
- For \(cz\) terms: \(-cz\), \(-3cz\), and \(5cz\)

### Step 3: Add the \(ax\) terms
\[ 3ax - 6ax - ax = (3 - 6 - 1)ax = -4ax \]

### Step 4: Add the \(by\) terms
\[ 5by + by - 2by = (5 + 1 - 2)by = 4by \]

### Step 5: Add the \(cz\) terms
\[ -cz - 3cz + 5cz = (-1 - 3 + 5)cz = 1cz = cz \]

### Step 6: Combine all results
Now, we combine the results from each step:
\[ -4ax + 4by + cz \]

### Final Answer
The sum of the given expressions is:
\[ -4ax + 4by + cz \]