Factorise:
`x^(2)-ax-bx + ab`

Answer

To factorise the expression \( x^2 - ax - bx + ab \), we can follow these steps:

### Step 1: Rearrange the expression
We start with the expression:
\[ x^2 - ax - bx + ab \]
We can rearrange it as:
\[ x^2 - ax - bx + ab = x^2 - (a + b)x + ab \]

### Step 2: Group the terms
Next, we can group the terms in pairs:
\[ (x^2 - (a + b)x) + ab \]

### Step 3: Factor by grouping
Now, we can factor out \( x \) from the first group:
\[ x(x - (a + b)) + ab \]

### Step 4: Recognize a common factor
Notice that we can rewrite \( ab \) as \( a(b - a) + b(a - b) \) to help us factor:
\[ x(x - (a + b)) + ab = (x - a)(x - b) \]

### Step 5: Final factorization
Thus, we can write the expression as:
\[ (x - a)(x - b) \]

### Final Answer
The factorised form of \( x^2 - ax - bx + ab \) is:
\[ (x - a)(x - b) \]

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