The Minus Version

A perfect square trinomial can have a negative middle term. Take x^2 - 10x + 25. Half of -10 is -5, and (-5)^2 = 25, which is the constant. So the test passes, and the trinomial factors as (x - 5)^2.

The rule is (a - b)^2 = a^2 - 2ab + b^2. The middle term is negative. The last term stays positive, because a square is never negative. Compare this with (a + b)^2 = a^2 + 2ab + b^2, where the middle term is positive.

Before you choose a rule, look at the middle term and the constant. A difference of squares has the form x^2 - a^2 = (x - a)(x + a). It has no middle term. A perfect square trinomial has the form x^2 ± 2ax + a^2 = (x ± a)^2. It has a middle term, and the sign of the middle term is the sign inside the square.