ROCK AND ROLL
Probably the most famous binomial is rock and roll. Why is rock and roll a binomial? Because it has two terms coordinated by a conjunction. In this case, the two terms are both verbs. The terms in binomials, however, can also be two nouns, two verbs, two prepositions, two adverbs or any mix of all the above. Also a binomial can occur with any conjunction, including but and or, and not just and.
Another important thing to know about binomials (and trinomials) is that it is a fixed expression with a fixed order. In other words, it would sound strange to say "I love roll and rock." Portuguese also has binomials such as vira e mexe, altos e baixos, indas e vindas, but they are not nearly as common as they are in English.
To discover the right/best way after making mistakes : Through trial and error
In today´s world: In this day and age
Maintain obedience in society: Keep law and order
Oferta e demanda: supply and demand
The basics for living: food and shelter
Can you think of any others?
Adapted from Como dizer tudo em inglês Avançado by Ron martinez