What mathematical pattern can be seen in a perfect square trinomial and how is the pattern used to factor the trinomi

(a ± b)² = a² ± 2ab + b² . . . . . . . (signs match)

The middle term is twice the product of the roots of the other two terms. This tells you the terms of the binomial are the square roots of the end terms.

The sign in the binomial will match the sign of the "2ab" term. The order of terms in the binomial doesn't matter. (a±b)² = (b±a)² when signs match.