Factorise :
`(a+b)^(3) -a-b`

Answer

To factorise the expression \((a+b)^{3} - a - b\), we will follow these steps:

### Step 1: Rewrite the expression
Start with the original expression:
\[ (a+b)^{3} - a - b \]

### Step 2: Group the terms
Notice that we can group the terms as follows:
\[ (a+b)^{3} - (a + b) \]

### Step 3: Factor out \((a+b)\)
Now, we can factor out \((a+b)\) from the expression:
\[ = (a+b) \left( (a+b)^{2} - 1 \right) \]

### Step 4: Recognize the difference of squares
The term \((a+b)^{2} - 1\) is a difference of squares, which can be factored further:
\[ = (a+b) \left( (a+b - 1)(a+b + 1) \right) \]

### Final Factored Form
Putting it all together, we have:
\[ = (a+b)(a+b-1)(a+b+1) \]

Thus, the final factorised form of \((a+b)^{3} - a - b\) is:
\[ (a+b)(a+b-1)(a+b+1) \]

---