Product of (f.g)(a) = (a² - 3a - 2)(18³ - 20a)

To find the product of (f.g)(a), we need to multiply the two functions f(a) = a² - 3a - 2 and g(a) = 18³ - 20a.

f(a) = a² - 3a - 2
g(a) = 18³ - 20a

Now, we can find the product of f(a) and g(a):

(f.g)(a) = f(a) * g(a)
(f.g)(a) = (a² - 3a - 2)(18³ - 20a)

Expanding the product:

(f.g)(a) = a² * 18³ - 3a * 18³ - 2 * 18³ - a² * 20a + 3a * 20a + 2 * 20a
(f.g)(a) = 18³a² - 54a² - 36 - 20a³ + 60a² + 40a

Combining like terms:

(f.g)(a) = 18³a² - 20a³ - 54a² + 60a² + 40a - 36
(f.g)(a) = -20a³ + 24a² + 40a - 36

Therefore, the product of (f.g)(a) is -20a³ + 24a² + 40a - 36.

Expanding the product:

```
(f.g)(a) = (a² - 3a - 2)(18³ - 20a)
```

```
= (a² - 3a - 2)(5832 - 20a)
```

```
= 5832a² - 20a5832 - 11664a + 60a²
```

```
= 5892a² - 11664a - 20a5832
```

Therefore, (f.g)(a) = 5892a² - 11664a - 20a5832.