Answer
$-(3x+10i)(3x-10i)$
Work Step by Step
The given expression, $ -9x^2-100 ,$ is equivalent to \begin{align*} & -(9x^2+100) \\&= -[9x^2-(-100)] \\&= -[9x^2-(-1\cdot100)] .\end{align*} Since $i^2=-1,$ the expression above is equivalent to \begin{align*} & -[9x^2-(i^2\cdot100)] \\&= -[9x^2-(100i^2)] .\end{align*} Using $a^2-b^2=(a+b)(a-b)$ or the factoring of the difference of $2$ squares, the expression above is equivalent to \begin{align*} & -[(3x)^2-(10i)^2] \\&= -[(3x+10i)(3x-10i)] \\&= -(3x+10i)(3x-10i) .\end{align*} Hence, the factored form of the given expression is $
-(3x+10i)(3x-10i)
.$
CHECKING: Multiplying the factors above results to
\begin{align*}
&
-[(3x+10i)(3x-10i)]
\\&=
-[(3x)^2-(10i)^2]
&\left(\text{use }(a+b)(a-b)=a^2-b^2\right)
\\&=
-(9x^2-100i^2)
\\&=
-9x^2+100i^2
\\&=
-9x^2+100(-1)
&\left(\text{use }i^2=-1\right)
\\&=
-9x^2-100
\text{ (same as original expression)}
.\end{align*}
