1. (x – 6)(x² + 6x + 36) = x³ – 6³ = x³ – 216.2. y³ – 64 = (y – 4)(y² + 4y + 16) ⇒ M = y² + 4y + 16.3.(a² + 2b³)(a⁴ – 2a²b³ + 4b⁶) = (a²)³ + (2b³)³ = a⁶ + 8b⁹.4. 3c² – 48 = 3(c² – 16) = 3(c – 4)(c + 4).5. 7a² – 42a + 63 = 7(a² – 6a + 9) = 7(a – 3)².6. a⁸ – a⁶ = a⁶(a² – 1) = a⁶(a – 1)(a + 1).7. m² – n² + m + n = (m – n)(m + n) + m + n = (m + n)(m – n + 1).8. x² – y² + 14y – 49 = x² – (y² – 14y + 49) = x² – (y – 7)² = (x – y + 7)(x + y – 7).9. 81a⁴ – 1 = ((3a)² – 1²)(9a² + 1) = (3a – 1)(3a + 1)(9a² + 1).10. 49x – x² = 0 ⇔ x(49 – x) = 0 ⇒ x ∈ {0, 49}.