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a³ + b³ = (a + b)(a² - ab + b²)
Ejemplo.
8 + y³ =
2² + y³ =
(2 + y)(2² - 2y + y²) =
(2 + y)(4 - 2y + y²)
27x³ + m⁶ =
3³x³ + (m²)³ =
(3x + m²)((3x)² +(3x)(m²) + (m²)²) =
(3x + m²)(3²x² + 3xm² + m⁴) =
(3x + m²)(9x² + 3xm² + m⁴)
Diferencia de cubos.
a³ - b³ = (a - b)(a² + ab + b²)
Ejemplo.
(n³z³ - 64x³) =
n³z³ - 4³x³) =
(nz - 4x)((nz)² + (nz)(4x) + (4x)²) =
(nz - 4x)(n²z² + 4nzx + 4²x²)
(nz - 4x)(n²z² + 4nzx + 16x²)