Quality Assurance: A set of activities designed to ensure 
that the development and/or maintenance process is adequate 
to ensure a system will meet its objectives.
Quality Assurance makes sure you are doing the right thing 
in the right way.

Software testing is the process used to measure the quality 
of developed computer software. Usually, quality is 
constrained to such topics as correctness, completeness, 
security, but can also include more technical requirements 
such as capability, reliability, 
efficiency, portability, maintainability, compatibility, 
and usability. Testing is a process of technical 
investigation, performed on behalf of stakeholders, that is 
intended to reveal quality-related information about the 
product with respect to the context in which it is intended 
to operate. 

Quality assurance , deals with "preventation" of defect 
when product being develped. It is associated with process 
and process improvement activities.

Testing meance Quality control , its focus defect detection 
and removal.

Quality control measures the Quality of product.

Quality Assurance measures the Quality of process when 
product being developed.