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

May 14, 2018

It's not a perfect square trinomial

#### Explanation:

A perfect square is expanded as

${\left(a + b\right)}^{2} = {a}^{2} + 2 a b + {b}^{2}$

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 $b$ ($2 a b$).

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