Factorise by grouping method :
`a^(3) + a - 3a^(2) - 3`

Answer

To factorise the expression \( a^3 + a - 3a^2 - 3 \) by the grouping method, we can follow these steps:

### Step 1: Rearrange the Expression
Rearrange the terms in the expression to make it easier to group:
\[ a^3 - 3a^2 + a - 3 \]

### Step 2: Group the Terms
Now, we can group the terms into two pairs:
\[ (a^3 - 3a^2) + (a - 3) \]

### Step 3: Factor Out Common Terms in Each Group
Now, we factor out the common terms from each group:
- From the first group \( a^3 - 3a^2 \), we can factor out \( a^2 \):
\[ a^2(a - 3) \]
- From the second group \( a - 3 \), we can factor out \( 1 \):
\[ 1(a - 3) \]

So, we rewrite the expression as:
\[ a^2(a - 3) + 1(a - 3) \]

### Step 4: Factor Out the Common Binomial
Now, we can see that \( (a - 3) \) is a common factor:
\[ (a - 3)(a^2 + 1) \]

### Final Result
Thus, the factorised form of the expression \( a^3 + a - 3a^2 - 3 \) is:
\[ (a - 3)(a^2 + 1) \]

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