Factorise
` x^(2) - 2y +xy -4`

Answer

To factorize the expression \( x^2 - 2y + xy - 4 \), we can follow these steps:

### Step 1: Rearrange the terms
We can rearrange the expression for convenience:
\[ x^2 + xy - 2y - 4 \]

### Step 2: Group the terms
Next, we can group the terms in pairs:
\[ (x^2 + xy) + (-2y - 4) \]

### Step 3: Factor out common factors from each group
From the first group \( (x^2 + xy) \), we can factor out \( x \):
\[ x(x + y) \]
From the second group \( (-2y - 4) \), we can factor out \(-2\):
\[ -2(y + 2) \]
So now we have:
\[ x(x + y) - 2(y + 2) \]

### Step 4: Rearrange the expression
Now we can rewrite the expression:
\[ x(x + y) - 2(y + 2) \]

### Step 5: Factor by grouping
Notice that \( (y + 2) \) can be factored out:
\[ (x - 2)(x + y + 2) \]

### Final Answer
Thus, the factorized form of the expression \( x^2 - 2y + xy - 4 \) is:
\[ (x - 2)(x + y + 2) \]

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