According to Omi and Winant, race is not just a socially constructed identity. It is a social concept that based on social, economic and institutional forces.
Also, race was the means for separating minority groups and justifying the inequality and moreover racial classification through out the history of mankind.
The link above goes to the article about the Boston Marathon Bombing and its relation to Racial Formation theory.
According to the article, Tamerlan Tsarnaev and Dzhokar Tsarnaev, the Chechens and also the criminals of the Boston Marathon Bombing are actually Caucasian by definition but
they were classified as non-Caucasian because of the notions of racial identity reproduced by the media in these days. This is the example of the concept of Racial Formation theory
because they were classfied by the social concept based on social (in this case, media) forces.
The link above goes to the article about the racial formation of Asian Americans during 19th and 20th century.
This article explains the racialization of nationality in the United States along with the history of Asian Americans and it means that they were the part of the minority group
which are the means for racial classification.