Answer
$b=\pm36$
Work Step by Step
$\bf{\text{Solution Outline:}}$
Use the concepts of the square of a binomial to find the missing term.
$\bf{\text{Solution Details:}}$
Using the square of a binomial which is given by $(a+b)^2=a^2+2ab+b^2$ or by $(a-b)^2=a^2-2ab+b^2,$ then the middle term of a perfect square trinomial is equal to half the product of the square roots of the first and third terms (can be positive or negative). Hence, the missing term of the given perfect square trinomial, $
4z^2+bz+81
,$ is
\begin{array}{l}\require{cancel}
b=\pm2(\sqrt{4})(\sqrt{81})
\\\\
b=\pm2(2)(9)
\\\\
b=\pm36
.\end{array}
