What is the advantage of treating protein samples with SDS and β-mercaptoethanol?

Proteins are insoluble in water and aggregate, which makes them ineffective for use in gel electrophoresis. 

SDS or sodium dodecyl sulfate is a strong detergent. When added to protein samples, SDS linearizes the protein, breaking up their 2 and 3 dimensional structure and coating them with a uniform negative charge. The SDS-coated, charged protein molecules are soluble in water, allowing them to be easily separated on application of an electrical current. 

β-mercaptoethanol effectively cleaves and reduces the numerous cysteine-cysteine disulphide bonds and irreversibly denatures the protein of interest. This prevents the proteins from digesting the RNA during the extraction process.