3m⁶ + 12m³n² + 12n⁴ - 27 = 3(m⁶ + 4m³n² + 4n⁴ - 9) = 3( (m³)² + 2*m³*(2n²) + (2n²)² - 3²) = 3((m³ + 2n²)² - 3²) = 3(m³ + 2n² + 3)(m³ + 2n² - 3)
a² - b² = (a - b)(a + b)
(a + b)² = a² + 2ab + b²
3m⁶ + 12m³n² + 12n⁴ - 27 = 3(m⁶ + 4m³n² + 4n⁴ - 9) = 3( (m³)² + 2*m³*(2n²) + (2n²)² - 3²) = 3((m³ + 2n²)² - 3²) = 3(m³ + 2n² + 3)(m³ + 2n² - 3)
a² - b² = (a - b)(a + b)
(a + b)² = a² + 2ab + b²