Ответ:

  1. \(214\cdot57=214\cdot(50+7)=10\,700+1\,498=12\,198\).
  2. \(509\cdot83=509\cdot(80+3)=40\,720+1\,527=42\,247\).
  3. \(3217\cdot51=3217\cdot(50+1)=160\,850+3\,217=164\,067\).
  4. \(5148\cdot670=5148\cdot67\cdot10=(5148\cdot(60+7))\cdot10=(308\,880+36\,036)\cdot10=3\,449\,160\).
  5. \(3154\cdot486=3154\cdot(500-14)=1\,577\,000-44\,156=1\,532\,844\).
  6. \(204\cdot305=204\cdot(300+5)=61\,200+1\,020=62\,220\).

Ответ: 1) 12 198; 2) 42 247; 3) 164 067; 4) 3 449 160; 5) 1 532 844; 6) 62 220.