no because it would be
if you knew that
ax^2+bx+c was a trinomial square, then the factored form would be
[tex]( \sqrt{a}x+ \sqrt{c})^{2} [/tex] or [tex]( \sqrt{a}x- \sqrt{c})^{2} [/tex]
so
if w^2-9w+81 is perfect square, factored form is either
[tex]( \sqrt{1}x+ \sqrt{81})^{2} [/tex] or [tex]( \sqrt{1}x- \sqrt{81})^{2} [/tex] aka [tex]( x+9)^{2} [/tex] or [tex]( x-9)^{2} [/tex]
expand them
(x+9)^2=x^2+18x+81, wron middle term
(x-9)^2=x^2-18x+81 wrong
so it is not
