Final answer:
The project management core area in question is called Quality Management, which encompasses planning, managing, and controlling the quality of a project's deliverables.
Step-by-step explanation:
The project management core area that includes plan quality management, manage quality, and control quality is commonly referred to as the Quality Management knowledge area.
This area is a key part of project management that ensures a project's deliverables meet the necessary quality standards throughout the project life cycle.
The process starts with planning quality management, which sets the quality objectives and how they will be achieved; managing quality ensures that the work is being performed according to the plan; and controlling quality involves monitoring specific project results to determine if they comply with relevant quality standards and identifying ways to eliminate causes of unsatisfactory performance.