Answer :
We can factor a perfect square trinomial as a perfect square like this:
[tex]A^2+2AB+B^2=(A+B)^2[/tex]Now, we have to find the values of A and B in our trinomial: 81x^2+bx+36, by making it look like the general above general form.
As we can see:
[tex]\begin{gathered} A^2+2AB+B^2=81x^2+bx+36 \\ \text{then:} \\ A^2=81x^2 \\ \text{then:} \\ A=\sqrt[]{81x^2}=\sqrt[]{81}\times\sqrt[]{x^2}=9x \\ \text{And} \\ B^2=36 \\ \text{Then:} \\ B=\sqrt[]{36}=6 \end{gathered}[/tex]Now we know that:
[tex]\begin{gathered} bx=2\times A\times B=2\times9x\times6=2\times9\times6\times x=108x \\ \text{then:} \\ \frac{bx}{x}=\frac{108x}{x} \\ b=108 \end{gathered}[/tex]And, when we factor our perfect square trinomial as a perfect square it looks like this:
[tex](9x+6)^2[/tex]