Verified answer

1)

(m² - n²) - (m - n) = (m + n)(m - n) - (m - n) = (m + n)(m - n - 1)

2)

-c² + c + d² + d = -(c - d)(c + d) + c + d² = (d² + c) - (c - d)(c + d)

3)

16x² - 4x - 25y² - 5y = 4x(4x - 1) - 25y² - 5y = 4x(4x - 1) - 5y(5y + 1) = (4x - 5y - 1)(4x + 5y)

4)

12a²b³ + 3a³b² + 16b² - a² = 3a²b²(4b + a) + 16b² - a² = 3a²b²(4b + a) + (4b + a)(4b - a) = (4b + a)(3a²b² + 4b - a)