Ответ:

  1. \(a^2-14a+49=(a-7)^2\);
  2. \(25y^2+10y+1=(5y+1)^2\);
  3. \(100a^2-180ab+81b^2=(10a-9b)^2\);
  4. \(16m^2+49n^2-56mn=(4m-7n)^2\);
  5. \(x^{10}-6x^5b+9b^2=(x^5-3b)^2\);
  6. \(36m^6+n^{12}+12m^3n^6=(6m^3+n^6)^2\).