Question

Is w^2-9w+81 a trinomial square

Answer 1

No because it would be
if you knew that
ax^2+bx+c was a trinomial square, then the factored form would be
$( \sqrt{a}x+ \sqrt{c})^{2}$ or $( \sqrt{a}x- \sqrt{c})^{2}$
so
if w^2-9w+81 is perfect square, factored form is either
$( \sqrt{1}x+ \sqrt{81})^{2}$ or $( \sqrt{1}x- \sqrt{81})^{2}$  aka $( x+9)^{2}$ or  $( x-9)^{2}$
expand them
(x+9)^2=x^2+18x+81, wron middle term

(x-9)^2=x^2-18x+81 wrong

so it is not