The Minus Version

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

The rule is $\left(a-b\right)^{2} = a^{2}-2ab+b^{2}$. The middle term is negative. The last term stays positive, because a square is never negative. Compare this with $\left(a+b\right)^{2} = a^{2}+2ab+b^{2}$, 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 $x^{2}-a^{2} = \left(x-a\right)\left(x+a\right)$. It has no middle term. A perfect square trinomial has the form $x^{2}\pm 2ax+a^{2} = \left(x\pm a\right)^{2}$. It has a middle term, and the sign of the middle term is the sign inside the square.