Given:
[tex]81m^2+25[/tex]
To factorize it completely over the set of complex numbers using the factoring pattern:
[tex]\begin{gathered} 81m^2+25=(9m)^2+(5)^2 \\ =(9m)^2-(i5)^2 \end{gathered}[/tex]
Using the formula,
[tex]a^2-b^2=(a+b)(a-b)_{}[/tex]
Hence, the factorized form is,
[tex](9m+5i)(9m-5i)[/tex]
