Factorise 49k2−56k+16 completely.

Sure, let's factorise the given expression step by step.

The given expression is 49k^2 - 56k + 16.

Step 1: Identify the common factor In this case, there is no common factor for all three terms.

Step 2: Check if it is a perfect square trinomial A perfect square trinomial is in the form (a^2 ± 2ab + b^2) which can be factored into (a ± b)^2.

In this case, the first term is (7k)^2, the third term is 4^2, and the middle term is 27k4 = 56k. So, it is a perfect square trinomial.

Step 3: Factorise the trinomial So, the factorised form of the given expression is (7k - 4)^2.