Розділ 3. Одночлени і многочлени » 43

Розкладіть на множники многочлен: 1) 2b5 + 6b + 3b4 + 9 = b4(2b + 3) + 3(2b + 3) = (2b + 3)(b4 + 3); 2) (5x + 1)3 – 64x3 = (5x + 1)3 – (4x)3 = (5x + 1 – 4x)((5x + 1)2 + (5x + 1) • 4x + (4x)2) = (x + 1)(25x2 + 10x + 1 + 20x2 + 4x + 16x2) = (x + 1)(61x2 + 14x + 1); 3) x5y2 – 5x3 + 35 – 7x2y2 = x2y2(x3 – 7) – 5(x3 – 7) = (x3 –7)(x2y2 – 5) 4) (–4a + 3xy)3 + 8x3y3 = (3xy – 4a)3 + (2xy)3 = (3xy – 4a+ 2xy)((3xy – 4a)2 – (3xy – 4a) • 2xy + 4x2y2) = (5xy – 4a)(9x2y2 – 24axy + 16a2 – 6x2y2 + 8axy + 4x2y2) = (5xy – 4a)(7x2y2 – 16axy + 16a2).