What value of k will make 4x^2 - 20x + k the square of a binomial?

Firstly, k must be a square number(1, 4, 9, ... etc.)

Next, we will analyze the second term of the trinomial.

-20x = $2\times 2x\times (\text{Something})$

$(\text{Something})= -5$

Next, we will find the square of that (Something).

$\boxed{(-a)^2=a^2}\\ (-5)^2=5^2=25$

Therefore k = 25.

4x^2 - 20x + 25 = $(2x)^2-2\times 2x \times (-5)+(-5)^2=(2x-5)^2$