Factor the polynomial 25t2+90t+81

$25t^2+90t+81$

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 $5t+92(5t)(9)=90t$.

Since 90t is the middle term of the trinomial, the trinomial is a perfect square. Therefore, $25t^2+90t+81=(5t+9{)}^2$