Question

В 34.10. Разложите на множители многочлен: 2) m³n³ + k³; 5) (a - b)³ + b³; 8) 27x³ — y³(x — y)8. 1) a³ - 27b3; 4) k® + (pq)6; 7) 8a³ + (a – b)3; DTTTIo 3) x® - y³; 6) (x - 2)³-27;​

Answer 1

m³n³ + k³ = (mn)³ + k³

(a - b)³ + b³ = (a - b + b)(a - b)² + b³ = (a - b)²(a - 2b) + b³

27x³ — y³(x — y)8 = (3x - y)(9x² + 3xy + y²(x - y)8)

a³ - 27b3 = (a - 3b)(a² + 3ab + 9b²)

k® + (pq)6 = (k® + p³q³)(k® - p³q³)

8a³ + (a – b)3 = (2a + (a - b))(4a² - 2ab + (a - b)²)

x® - y³ = (x - y)(x² + xy + y²)

(x - 2)³-27 = (x - 5)(x² - 4x + 13)