Question

Factor completely over the set of complex numbers using the factoring pattern Show all work

Answer 1

Given:

`81m^2+25`

To factorize it completely over the set of complex numbers using the factoring pattern:

`\begin{gathered} 81m^2+25=(9m)^2+(5)^2 \\ =(9m)^2-(i5)^2 \end{gathered}`

Using the formula,

`a^2-b^2=(a+b)(a-b)_{}`

Hence, the factorized form is,

`(9m+5i)(9m-5i)`