分散 and 散乱: distribution and a scattered state
Compare luggage split between two cars with branches scattered after a strong wind, without making intention or an accident a defining condition.
分散 focuses on distribution among places
分散 (ぶんさん) focuses on spreading things among several places. The example describes distributing them rather than keeping them together in one place.
“危険を分散するため荷物を二台の車に分けた。” says that luggage was split between two cars to spread the risk. It states that two cars were used, without saying that they held equal amounts.
散乱 describes things lying scattered about
散乱 (さんらん) describes things scattered here and there. In this example, the focus is the state of branches in a garden.
“強風の後、庭に枝が散乱していた。” says that branches were scattered across the garden after a strong wind. 散乱していた describes the scattered state at that time.
Keep the example’s circumstances separate from a definition
The luggage example states a purpose of spreading risk, while the branch example gives the setting after a strong wind. This does not make 分散 always intentional or 散乱 always the result of an accident.
Ask whether the focus is distribution among places or a scattered state. This comparison does not explain equal shares, mathematical variance, or the scattering of light.
What does the luggage example tell you, and can you infer equal amounts in the two cars?
Show the answer and why
It tells you that the luggage was split between two cars to spread the risk. It does not state equal amounts. The garden example instead foregrounds the state of branches lying scattered about.