1) x - 3y + x² - 9y² = (x - 3y) + (x - 3y)(x + 3y) = (x - 3y)(1 + x + 3y)
2) 9m² + 6mn + n² - 25 = (3m + n)² - 5² = (3m + n - 5)(3m + n + 5)
3) ab⁵ - b⁵ - ab³ + b³ = b⁵(a - 1) - b³(a - 1) = (a - 1)(b⁵ - b³) = (a - 1)b³(b² - 1) = (a - 1)b³(b - 1)(b + 1)
4) 1 - x² + 10xy - 25y² = 1 - (x² - 10xy + 25y²) = 1 - (x - 5y)² = (1 - (x - 5y))(1 + (x - 5y)) = (1 - x + 5y)(1 + x - 5y)