Factorise m2+24mn+144n2 completely.

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

1. The given expression is m^2 + 24mn + 144n^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 m^2 is m, the square root of 144n^2 is 12n, and 2m12n equals 24mn, which is the middle term.

4. Therefore, the factorised form of the given expression is (m + 12n)^2.