Ответ:

  1. \(x^{1/2}+x=x^{1/2}(1+x^{1/2})\);
  2. \((ab)^{1/3}+(ac)^{1/3}=a^{1/3}(b^{1/3}+c^{1/3})\);
  3. \(y^{3/4}-y^{1/8}=y^{1/8}(y^{5/8}-1)\);
  4. \(12xy^{2/3}-3x^{1/2}y=3x^{1/2}y^{2/3}(4x^{1/2}-y^{1/3})\).