Question

is this trinomial a trinomial square x^2+18x+81

Answer 1

Yes, it is a perfect square
.
Since the coefficient (multiplier) of the x^2 term is 1, the first term can only be factored
to x times x. This means the two factors of x^2 + 18x + 81 must be of the form:
.
(x + ____)*(x + ____)
.
The blanks must be a factor pair of 81. The only pairs of factors of 81 are 81*1 and 9*9.
If you fill the blanks of the factors ... for checking ... with the pair of 9's you get:


.
(x + 9)*(x + 9)
.
If you multiply these out you will get x^2 + 18x + 81.
.
But note that (x + 9)*(x + 9) = (x + 9)^2
.
So the trinomial is equal to (x + 9)^2 and is, therefore, a perfect square.
.
Hope this helps you to understand the problem.

Answer 2

it is if the square root of the last number = half the coefficient of x