Facts are statements that can be definitely proven using objective data. The statement that is a fact is absolutely valid. In other words, the statement can be pronounced as true or false. For example, 2 + 2 = 4. This expression identifies a true statement, or a fact, because it can be proved with objective data.
Opinions are personal views, or judgments. An opinion is what an individual believes about a particular subject. However, an opinion in argumentation must have legitimate backing; adequate evidence and credibility should support the opinion. Consider the credibility of expert opinions. Experts in a given field have the knowledge and credentials to make their opinion meaningful to a larger audience.
For example, you seek the opinion of your dentist when it comes to the health of your gums, and you seek the opinion of your mechanic when it comes to the maintenance of your car. Both have knowledge and credentials in those respective fields, which is why their opinions matter to you. Conversely, the authority of your dentist may be greatly diminished should he or she offer an opinion about your car, and vice versa.
In writing, you want to strike a balance between credible facts and authoritative opinions. Relying on one or the other will likely lose more of your audience than it gains.
The word prove is frequently used in the discussion of persuasive writing. Writers may claim that one piece of evidence or another proves the argument, but proving an argument is often not possible. No evidence proves a debatable topic one way or the other; that is why the topic is debatable. Facts can be proved, but opinions can only be supported, explained, and persuaded.