Answer :
we have the expression
[tex]\begin{gathered} 9p^2+6p+1-q^2 \\ (9p^2+6p)+(1-q^2) \\ 9(p^2+\frac{2}{3}p)+(1-q^2) \\ 9(p^2+\frac{2}{3}p+\frac{p^2}{9})-p^2+(1-q^2) \\ 9(p+\frac{p}{3})^2+(1-q)(1+q)-p^2 \end{gathered}[/tex]we have the expression
[tex]\begin{gathered} 9p^2+6p+1-q^2 \\ (9p^2+6p)+(1-q^2) \\ 9(p^2+\frac{2}{3}p)+(1-q^2) \\ 9(p^2+\frac{2}{3}p+\frac{p^2}{9})-p^2+(1-q^2) \\ 9(p+\frac{p}{3})^2+(1-q)(1+q)-p^2 \end{gathered}[/tex]