Question 890961
"sum or difference of two squares", from a trinomial?  Not likely.


{{{(1/4)(x^2+16x+36)}}}, assuming your "1/4" is a factor for the x^2 term only.  (You showed no other grouping symbols.)


Square term to Complete the Square is {{{(16/2)^2=64}}}.
{{{(x^2+16x+64-64+36)}}}
{{{(x+8)^2-28}}}
The best you can do for what you ask is {{{((x+8)-sqrt(28))((x+8)+sqrt(28))}}} to represent your difference of two squares.  Maybe this means that what you wanted were  {{{(x+8)^2-(sqrt(28))^2}}}.