Here are some ways to think about it:
* To champion: You "expouse" a cause you believe in strongly and publicly defend it.
* To embrace: You "expouse" a belief by accepting it wholeheartedly and making it your own.
* To propagate: You "expouse" a view by spreading it and encouraging others to adopt it.
Example:
* "The politician expoused his views on healthcare reform during his speech."
* "The author expoused the importance of environmental conservation in her book."
Remember: The word "expouse" always implies a public or active support of a cause or belief.