Factorise h2+6hk+9k2 completely.

Sure, here is the step-by-step solution:

1. The given expression is h^2 + 6hk + 9k^2.

2. This is a perfect square trinomial, which can be written in the form (a + b)^2, where a is the square root of the first term, b is the square root of the last term, and 2ab is the middle term.

3. The square root of h^2 is h, the square root of 9k^2 is 3k, and 2h3k equals 6hk, which is the middle term.

4. Therefore, the factorised form of the expression h^2 + 6hk + 9k^2 is (h + 3k)^2.