#### Answer

Prime

#### Work Step by Step

RECALL:
A perfect square trinomial can be factored using either of the following formulas:
(i) $a^2+2ab+b^2=(a+b)^2$; or
(ii) $a^2-2ab+b^2=(a-b)^2$
The given trinomial can be written as:
$=x^2-9xy + (9y)^2$
This trinomial is not similar to any of the perfect square trinomials in (i) and (ii).
Thus, this trinomial is NOT a perfect square trinomial.
This trinomial has a leading coefficient of 1.
A quadratic trinomial with a leading coefficient of $1$ can be factored only if there are factors of the numerical coefficient of the third term whose sum is equal to the numerical coefficient of the middle term.
However, $81$ has no pair of factors whose sum is equal to $-9$.
There are also no common factors for the terms in the trinomial.
This means that the given trinomial is prime.