Final answer:
The perfect square trinomial 81y²+72y+16 can be factored completely as (9y+4)².
Step-by-step explanation:
To factor the perfect square trinomial 81y²+72y+16 completely, we need to recognize that it is in the form of (a+b)², where a and b are the binomial factors. In this case, a is √81y² which simplifies to 9y, and b is √16 which simplifies to 4. Therefore, the factored form of the trinomial is (9y+4)².