Factorise :
`a^(2) - 3a - 40`

Answer

To factorise the expression \( a^2 - 3a - 40 \), we will follow these steps:

### Step 1: Identify the expression
We start with the expression:
\[ a^2 - 3a - 40 \]

### Step 2: Split the middle term
We need to find two numbers that multiply to \(-40\) (the constant term) and add up to \(-3\) (the coefficient of the middle term).

The two numbers that satisfy this condition are \(-8\) and \(5\) because:
\[ -8 \times 5 = -40 \quad \text{and} \quad -8 + 5 = -3 \]

### Step 3: Rewrite the expression
Now we can rewrite the expression by splitting the middle term:
\[ a^2 - 8a + 5a - 40 \]

### Step 4: Group the terms
Next, we group the terms:
\[ (a^2 - 8a) + (5a - 40) \]

### Step 5: Factor out the common terms
Now, we factor out the common factors from each group:
\[ a(a - 8) + 5(a - 8) \]

### Step 6: Factor out the common binomial
Now we can factor out the common binomial \((a - 8)\):
\[ (a - 8)(a + 5) \]

### Final Answer
Thus, the factorised form of the expression \( a^2 - 3a - 40 \) is:
\[ \boxed{(a - 8)(a + 5)} \]

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