Answer
This polynomial is prime.
Work Step by Step
$ 9x^{2}+48xy+64y^2$
This polynomial is prime because the formula for a perfect square trinomial states that
$(A\pm B)^{2}=A^{2}\pm 2AB+B^{2}$
In the given example, $2AB\ne48xy$
If it were a perfect square trinomial, the middle term would be $48xy$.
