Factorise: `ax - bx+ ay- by`

Answer

To factorise the expression \( ax - bx + ay - by \), we can follow these steps:

### Step 1: Group the terms
We can rearrange the expression by grouping the terms:
\[ (ax - bx) + (ay - by) \]

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

### Step 3: Write the expression with the factored terms
Now, we can rewrite the expression using the factored terms:
\[ x(a - b) + y(a - b) \]

### Step 4: Factor out the common factor
Notice that \( (a - b) \) is a common factor in both terms. We can factor it out:
\[ (a - b)(x + y) \]

### Final Answer
Thus, the factorised form of the expression \( ax - bx + ay - by \) is:
\[ (a - b)(x + y) \]

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