Question

How do you know if `25b^2 − 45b − 81` is a perfect square trinomial and how do you factor it?

Answer 1

It's not a perfect square trinomial

Explanation:

A perfect square is expanded as

`(a+b)^2 = a^2 + 2ab + b^2`

So, you must check if you have two perfect squares with positive sign (`a^2` and `b^2`), and if the third term is twice the product of `a` and `b` (`2ab`).

In your case, you only have one perfect square, which is `25b^2` (square of `5b`), but the other square (`81=9^2`) has a negative sign. So, this is not a perfect square trinomial.