Factorise :
` a^(2) + bc- ac - b^(2)`

Answer

To factorize the expression \( a^2 + bc - ac - b^2 \), we can follow these steps:

### Step 1: Rearrange the expression
We start by rearranging the terms in the expression:
\[ a^2 - b^2 + bc - ac \]

### Step 2: Group the terms
Next, we group the terms into two pairs:
\[ (a^2 - b^2) + (bc - ac) \]

### Step 3: Factor out the common factors
Now, we can factor each group:
1. The first group \( a^2 - b^2 \) is a difference of squares, which can be factored as:
\[ (a - b)(a + b) \]
2. In the second group \( bc - ac \), we can factor out \( c \):
\[ c(b - a) \]

So, we rewrite the expression as:
\[ (a - b)(a + b) + c(b - a) \]

### Step 4: Factor out the common binomial
Notice that \( (b - a) \) can be rewritten as \( -(a - b) \). Thus, we can factor out \( (a - b) \):
\[ (a - b)(a + b - c) \]

### Final Factored Form
The final factored form of the expression \( a^2 + bc - ac - b^2 \) is:
\[ (a - b)(a + b - c) \]