Which of the following describes very large amounts of blood being expelled with a cough?

The term that describes the expulsion of very large amounts of blood while coughing is hemoptysis. This condition involves the coughing up of blood that originates from the respiratory tract, specifically the lungs or the bronchi.

Understanding the other options helps clarify why hemoptysis is the correct choice. Hematuria refers to blood in the urine, which indicates a urinary tract issue rather than a respiratory one. Hematochezia denotes the passage of fresh blood through the anus, typically associated with lower gastrointestinal bleeding. Epistaxis, commonly known as a nosebleed, involves bleeding from the nasal passages and does not relate to coughing.

Therefore, hemoptysis is distinctively linked to coughing up blood, making it the correct answer in this context.