And put no difference ... - Though they had not been circumcised, and though they did not conform to the Law of Moses. Thus, God showed that the observance of these rites was not necessary in order to the true conversion of people, and to acceptance with him. He did not give us, who are Jews, any advantage over them, but justified and purified all in the same manner.
Purifying their hearts - Thus, giving the best evidence that he had renewed them, and admitted them to favor with him.
By faith - By believing on the Lord Jesus Christ. This demonstrated that the plan on which God was now about to show favor to people was not by external rites and ceremonies, but by a scheme which required faith as the only condition of acceptance. It is further implied here that there is no true faith which does not purify the heart.