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

1 Answer
May 14, 2018

Answer:

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.