Add :
`5a + 3b, a - 2b, 3a + 5b`

Answer

To solve the problem of adding the algebraic expressions \(5a + 3b\), \(a - 2b\), and \(3a + 5b\), we can follow these steps:

### Step 1: Write down the expressions
We start with the three expressions:
\[ 5a + 3b, \quad a - 2b, \quad 3a + 5b \]

### Step 2: Combine like terms
Next, we group the like terms together. The terms with \(a\) are \(5a\), \(a\), and \(3a\). The terms with \(b\) are \(3b\), \(-2b\), and \(5b\).

So we can rewrite the expression as:
\[ (5a + a + 3a) + (3b - 2b + 5b) \]

### Step 3: Simplify the \(a\) terms
Now, we simplify the \(a\) terms:
\[ 5a + a + 3a = 5a + 1a + 3a = (5 + 1 + 3)a = 9a \]

### Step 4: Simplify the \(b\) terms
Next, we simplify the \(b\) terms:
\[ 3b - 2b + 5b = (3 - 2 + 5)b = 6b \]

### Step 5: Combine the results
Now we combine the simplified \(a\) and \(b\) terms:
\[ 9a + 6b \]

### Final Answer
The final result after adding the expressions is:
\[ \boxed{9a + 6b} \]

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