Answer
$(-\infty,-8) $.
Work Step by Step
Step 1. For $x^3+8x^2\lt0 \Longrightarrow x^2(x+8)\lt0$, identify boundary points as $x=-8,0$.
Step 2. Form intervals $(-\infty,-8),(-8,0),(0,\infty)$.
Step 3. Choose test values for each interval $x=-9,-1,1$.
Step 4. Test the inequality to get results: $True,\ False,\ False$
Step 5. We have the solution $(-\infty,-8) $.
