Factorise 4k2−4k+1 completely.

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

Step 1: Identify the coefficients of the quadratic equation. In this case, a = 4, b = -4, and c = 1.

Step 2: Check if the equation is a perfect square trinomial. A perfect square trinomial is in the form (ax)^2 - 2abx + b^2. In this case, (2k)^2 - 22k1 + 1^2 = 4k^2 - 4k + 1, so it is a perfect square trinomial.

Step 3: Factorise the equation. The factorised form of a perfect square trinomial is (ax - b)^2. So, the factorised form of 4k^2 - 4k + 1 is (2k - 1)^2.

So, the factorised form of 4k^2 - 4k + 1 is (2k - 1)^2.