Catalyzes the addition of GlcNAc or GlcUA monosaccharides to the nascent hyaluronan polymer. Therefore, it is essential to hyaluronan synthesis a major component of most extracellular matrices that has a structural role in tissues architectures and regulates cell adhesion, migration and differentiation (By similarity). This is one of three isoenzymes responsible for cellular hyaluronan synthesis and it is particularly responsible for the synthesis of high molecular mass hyaluronan (By similarity). [hyaluronan](n) + UDP-N-acetyl-alpha-D-glucosamine = H(+) + N-acetyl-beta-D-glucosaminyl-(1->4)-[hyaluronan](n) + UDP N-acetyl-beta-D-glucosaminyl-(1->4)-[hyaluronan](n) + UDP-alpha-D-glucuronate = [hyaluronan](n+1) + H(+) + UDP Glycan biosynthesis; hyaluronan biosynthesis. Homodimer; dimerization promotes enzymatic activity. Travels from endoplasmic reticulum (ER), Golgi to plasma membrane and either back to endosomes and lysosomes, or out into extracellular vesicles. Post-translational modifications control HAS2 trafficking. Belongs to the NodC/HAS family.