Factorise : (ii) `a^2 - (b+5) a + 5b`

Answer

To factorise the expression \( a^2 - (b + 5)a + 5b \), we can follow these steps:

### Step 1: Rewrite the expression
We start with the expression:
\[ a^2 - (b + 5)a + 5b \]
This can be rewritten as:
\[ a^2 - (b + 5)a + 5b = a^2 - ba - 5a + 5b \]

### Step 2: Rearrange the terms
Now, we can rearrange the terms:
\[ a^2 - ba - 5a + 5b \]

### Step 3: Group the terms
Next, we group the terms in pairs:
\[ (a^2 - ba) + (-5a + 5b) \]

### Step 4: Factor out the common terms
Now, we can factor out the common terms from each group:
- From the first group \( a^2 - ba \), we can factor out \( a \):
\[ a(a - b) \]
- From the second group \( -5a + 5b \), we can factor out \( -5 \):
\[ -5(a - b) \]

### Step 5: Combine the factors
Now we can combine the factored terms:
\[ a(a - b) - 5(a - b) \]
Notice that \( (a - b) \) is a common factor:
\[ (a - b)(a - 5) \]

### Final Answer
Thus, the factorised form of the expression \( a^2 - (b + 5)a + 5b \) is:
\[ (a - b)(a - 5) \]

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