1) 4a⁴ - 25d⁴ = (2a²)² - (5d²)² = (2a² - 5d²)(2a² + 5d²)

2) a²b⁴ - c⁴d² = (ab²)² - (c²d)² = (ab² - c²d)(ab² + c²d)

3) a⁴ - b⁸ = (a²)² - (b⁴)² = (a² - b⁴)(a² + b⁴)

4) b⁴ - 81 = (b²)² - 9² = (b² - 9)(b² + 9)

5) a²⁰ - b³⁰ = (a¹⁰)² - (b¹⁵)² = (a¹⁰ - b¹⁵)(a¹⁰ + b¹⁵)