Factorise 3a2+36a+81 completely.

Sure, here are the steps to factorise the given expression:

1. The given expression is 3a^2 + 36a + 81.

2. First, we can factor out the greatest common factor (GCF), which is 3. This gives us 3(a^2 + 12a + 27).

3. Now, we need to factorise the quadratic expression a^2 + 12a + 27. We are looking for two numbers that multiply to 27 and add to 12. The numbers 3 and 9 fit these criteria.

4. Therefore, a^2 + 12a + 27 can be factorised as (a + 3)(a + 9).

5. So, the completely factorised form of the given expression is 3(a + 3)(a + 9).