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

Answer

To factorise the expression \( a^3 + b^3 + a + b \), we can follow these steps:

### Step 1: Recognize the sum of cubes
We know that \( a^3 + b^3 \) can be factored using the identity:
\[ a^3 + b^3 = (a + b)(a^2 - ab + b^2) \]
So, we can rewrite our expression as:
\[ a^3 + b^3 + a + b = (a + b)(a^2 - ab + b^2) + a + b \]

### Step 2: Factor out the common term
Notice that both terms in the expression now contain \( (a + b) \):
\[ = (a + b)(a^2 - ab + b^2) + 1(a + b) \]
We can factor out \( (a + b) \):
\[ = (a + b)(a^2 - ab + b^2 + 1) \]

### Step 3: Write the final factorized form
Thus, the factorized form of the expression \( a^3 + b^3 + a + b \) is:
\[ \boxed{(a + b)(a^2 - ab + b^2 + 1)} \]

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