Verified answer

1) a³b⁶ - c³ = (ab²)³ - c³ = (ab² - c)(a²b⁴ + ab²c + c²)

2) 3ax³ - 3ay³ = 3a(x³ - y³) = 3a(x - y)(x² + xy + y²)

3) 12am³ - 12an³ = 12a(m³ - n³) = 12a(m - n)(m² + mn + n²)

4) a⁶b³ + 27 = (a²b)³ + 3³ = (a²b + 3)(a⁴b² - 3a²b + 9)

5) 1 - p⁹ = 1³ - (p³)³ = (1 - p³)(1 + p³ + p⁶)

6) 64x³y⁶ + 343a³ = (4xy²)³ + (7a)³ = (4xy² + 7a)(16x²y⁴ - 28axy² + 49a²)