A perfect square trinomial is a type of polynomial that can be expressed as the square of a binomial. It takes the form (a + b)^2 or (a - b)^2, which expands to a^2 + 2ab + b^2 or a^2 - 2ab + b^2. The key characteristic is that the first and last terms are perfect squares, while the middle term is twice the product of the square roots of these terms. For example, the trinomial x^2 + 6x + 9 is a perfect square because it can be factored into (x + 3)^2. Recognizing perfect square trinomials is useful in algebra for simplifying expressions and solving equations. They often appear in various mathematical contexts, including quadratic equations and factoring techniques.