Вправи 701 - 837 » 814

Подайте у вигляді куба двочлена вираз: 1) a3 + 3a2 + 3a + 1 = (a3 + 1) + (3a2 + 3a) = (a + 1)(a2 – 2 + 1) + 3a(a + 1) = (a + 1)(a2 – a + 1 + 3a) = (a + 1)(a2 + 2a + 1) = (a + 1)2 = (a + 1)3; 2) b3 – 6b2 + 12b – 8 = (b3 – 8) – (6b2 – 12b) = (b – 2)(b2 – 2b + 4) – 6b(b – 2) = (b – 2)(b2 + 2b + 4 – 6b) = (b – 2)(b2 – 4b + 4) = (b – 2)(b – 2)2 = (b – 2)3.