Fractorise:
`25 -a^(2) -b ^(2) - 2ab`

Answer

To factorize the expression \( 25 - a^2 - b^2 - 2ab \), we can follow these steps:

### Step 1: Rewrite the expression
We start with the expression:
\[ 25 - a^2 - b^2 - 2ab \]
We can rearrange it to group the \( a^2 \), \( b^2 \), and \( 2ab \) terms together:
\[ 25 - (a^2 + b^2 + 2ab) \]

### Step 2: Recognize a perfect square
Notice that \( a^2 + b^2 + 2ab \) can be rewritten as a perfect square:
\[ a^2 + b^2 + 2ab = (a + b)^2 \]
Thus, we can rewrite the expression as:
\[ 25 - (a + b)^2 \]

### Step 3: Rewrite 25 as a perfect square
Next, we recognize that \( 25 \) can also be expressed as a perfect square:
\[ 25 = 5^2 \]
So we can rewrite the expression as:
\[ 5^2 - (a + b)^2 \]

### Step 4: Apply the difference of squares formula
Now we can apply the difference of squares formula, which states that \( x^2 - y^2 = (x - y)(x + y) \). Here, let \( x = 5 \) and \( y = (a + b) \):
\[ 5^2 - (a + b)^2 = (5 - (a + b))(5 + (a + b)) \]

### Step 5: Simplify the expression
This simplifies to:
\[ (5 - a - b)(5 + a + b) \]

### Final Answer
Thus, the factorized form of the expression \( 25 - a^2 - b^2 - 2ab \) is:
\[ (5 - a - b)(5 + a + b) \]

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