\({x^2 - 2xy + y^2}\)
I never encountered a trinomial like this before... how should I factor it?
This is something called a PERFECT SQUARE TRINOMIAL (PST). It is, well, the square of a binomial. These are the two forms:
\((x+y)^2=x^2+2xy+y^2\)
\((x-y)^2=x^2-2xy+y^2\)
So, the factored form of your trinomial is \((x-y)^2\)