factorise `ax-bx+a^(2)-ab`

Answer

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

### Step 1: Group the terms
We start with the expression:
\[ ax - bx + a^2 - ab \]
We can group the first two terms and the last two terms:
\[ (ax - bx) + (a^2 - ab) \]

### Step 2: Factor out common terms from each group
In the first group \( ax - bx \), we can factor out \( x \):
\[ x(a - b) \]
In the second group \( a^2 - ab \), we can factor out \( a \):
\[ a(a - b) \]

### Step 3: Combine the factored terms
Now we can rewrite the expression using the factored forms:
\[ x(a - b) + a(a - b) \]
Notice that \( (a - b) \) is common in both terms.

### Step 4: Factor out the common binomial
Now we can factor out \( (a - b) \):
\[ (a - b)(x + a) \]

### Final Result
Thus, the factorized form of the expression \( ax - bx + a^2 - ab \) is:
\[ (a - b)(x + a) \]

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