"encapsulates the idea" is correct and usable in written English.
You can use it when you want to explain that a phrase or expression summarizes an idea in a concise, succinct way. For example, "Her quote, 'Find joy in the journey,' encapsulates the idea that life is more enjoyable when we don't focus solely on the end goal."
His own life story encapsulates the idea.
It encapsulates the idea of removal from the source, just constant layers of signal degradation.
This principle might be relevant to other areas of life and encapsulates the idea of rights and responsibilities.
According to Time Out, the quote used on the T-shirts encapsulates the "idea of finding your voice, keeping your nerve and fighting the impulse to be a 'good girl'" – a powerful theme in the film.
Popularised by Archbishop Desmond Tutu and Nelson Mandela as a way to heal post-apartheid South Africa, the ancient Bantu word encapsulates the idea of shared humanity: "I am, because we all are".
It encapsulates the idea that all the particles of matter in the universe attract each other through the force of gravity – Newton's law tells us how strong that attraction is.
It telegraphs not money but access, ethics, culture — encapsulating the idea psychologist Daniel Gilbert popularized that happiness grows more through experiences than purchases.
Still, in rattling off the journalistic competition he admires, Hughes audibly winced over including BuzzFeed, which has become a Pavlovian stand-in through which the uninformed – even among former TNR staff – encapsulate the idea of "declining standards" in journalism.
For him, the saying encapsulated the idea that a good treaty would require rigorous inspections, to insure that neither side was dragging its feet or, worse, disposing of decoy bombs, rather than real ones.
The term twenty-first century learning is widely used to encapsulate the idea that fundamental changes in the nature of learning and education have occurred in the twenty-first century as a consequence of rapidly changing technologies and globalisation (Kereluik, Mishra, Fahnoe, & Terry, 2013).
One of my first tasks as a content manager was to choose a book that would encapsulate the idea of a visual smorgasbord of references.
