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

Answer

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

### Step 1: Write the expression
We start with the expression:
\[ a^2 - b^2 - (a + b)^2 \]

### Step 2: Expand \( (a + b)^2 \)
Using the formula for the square of a binomial, we expand \( (a + b)^2 \):
\[ (a + b)^2 = a^2 + 2ab + b^2 \]
Substituting this back into the expression gives:
\[ a^2 - b^2 - (a^2 + 2ab + b^2) \]

### Step 3: Simplify the expression
Now, we simplify the expression:
\[ a^2 - b^2 - a^2 - 2ab - b^2 \]
The \( a^2 \) terms cancel out:
\[ -b^2 - 2ab - b^2 = -2b^2 - 2ab \]

### Step 4: Factor out the common term
Now we can factor out \(-2\) from the expression:
\[ -2(b^2 + ab) \]

### Step 5: Factor further if possible
We can factor \( b \) out of the remaining expression:
\[ -2b(b + a) \]

### Final Result
Thus, the factorised form of the expression \( a^2 - b^2 - (a + b)^2 \) is:
\[ -2b(b + a) \]

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