Final answer:
A perfect square trinomial is a trinomial expression that can be factored into a perfect square binomial. The first and last terms must be perfect squares, and the middle term must be twice the product of the square roots of the first and last terms.
Step-by-step explanation:
A perfect square trinomial is a trinomial expression that can be factored into a perfect square binomial. To determine if a trinomial is a perfect square trinomial, we can use the following criteria:
- The first and last terms must be perfect squares.
- The middle term must be twice the product of the square roots of the first and last terms.
For example, let's consider the trinomial x^2 + 6x + 9. The first term x^2 is a perfect square (x^2 = (x)^2) and the last term 9 is also a perfect square (9 = 3^2). The middle term 6x is twice the product of the square roots of the first and last terms (6x = 2(x)(3)). Therefore, x^2 + 6x + 9 is a perfect square trinomial.