Final answer:
The perfect square trinomial among the given options is a^(2)-4a+16. It fulfills the criteria of a perfect square trinomial, with both the first and last terms being perfect squares and the middle term being twice the product of the square roots of the first and last terms.
Step-by-step explanation:
The trinomial that is a perfect square trinomial among the given options is a^(2)-4a+16.
A perfect square trinomial is a special kind of trinomial that can be factored into identical binomials. For a trinomial to be a perfect square, the first term and the last term must be perfect squares and the middle term must be twice the product of the square roots of the first and last terms.
In a^(2)-4a+16, the first term, a^2, is a square, the last term, 16, is a square and the middle term, -4a, is double the product of the square roots of the first and last terms. Thus, this trinomial meets the criteria to be a perfect square trinomial.
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