Question

how did you express each perfect square trinomial as the square of a binomial?

Answer 1

(x + a)^2 = x^2 + 2ax + a^2 so if the leading term is x^2 (the coefficient is1) then it's very easy. Look at the coefficient of x and divide it by 2. That's a. As a check, the constant term should be a^2. 

x^2 + 6x + 9 = (x + 3)^2. The +3 is half of the +6 coefficient. The last term is 3^2. 
x^2 - 10x + 25 = (x - 5)^2. The -5 is half of the -10 coefficient. The last term is (-5)^2.