Fractorise:
`x ^(2) - x (a + 2b) + 2ab `

Answer

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

### Step 1: Rewrite the expression
Start with the original expression:
\[ x^2 - x(a + 2b) + 2ab \]

### Step 2: Expand the middle term
Distribute \( -x \) in the middle term:
\[ x^2 - ax - 2bx + 2ab \]

### Step 3: Rearrange the terms
Rearranging the terms gives us:
\[ x^2 - ax - 2bx + 2ab \]

### Step 4: Group the terms
Now, we can group the first two terms and the last two terms:
\[ (x^2 - ax) + (-2bx + 2ab) \]

### Step 5: Factor out the common factors
From the first group \( (x^2 - ax) \), we can factor out \( x \):
\[ x(x - a) \]
From the second group \( (-2bx + 2ab) \), we can factor out \( -2b \):
\[ -2b(x - a) \]

### Step 6: Combine the factored terms
Now we have:
\[ x(x - a) - 2b(x - a) \]
Notice that \( (x - a) \) is common in both terms, so we can factor it out:
\[ (x - a)(x - 2b) \]

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

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