\(25t^2 + 90t + 81\)
We have perfect squares: \(25t^2 = (5t)^2\) and \(81 = 9^2\)
To factor as a perfect square trinomial, take twice the product of the two terms in the binomial \(5t + 9 2(5t)(9) = 90t\).
Since 90t is the middle term of the trinomial, the trinomial is a perfect square. Therefore, \(25t^2 + 90t + 81 = (5t + 9)^2\)