Разложение на множители суммы и разности кубов

m³n³-1=

1+q³p³=

27-a³b³=

p⁶-q³=

m³+n¹²=

x³-y⁶ =

m³n³-1 = (mn) ³-1³ = (mn-1) ((mn) ²+mn*1+1²) = (mn-1) (m²n²+mn+1)

1+q³p³ = (1+qp) (1-pq+q²p²) = (1+pq) (1-pq+p²q²)

27-a³b³=3³ - (ab) ³ = (3-ab) (3²+3ab + (ab) ²) = (3-ab) (9+3ab+a²b²)

p⁶-q³=p³ˣ²-q³ = (p²) ³-q³ = (p²-q) ((p²) ²+p²q+q²) = (p²-q) (p⁴+p²q+q²)

m³+n¹²=m³+n³ˣ⁴=m³ + (n⁴) ³ = (m+n⁴) (m²-mn⁴ + (n⁴) ²) = (m+n⁴) (m²-mn⁴+n⁸)

x³-y⁶=x³-y³ˣ²=x³ - (y²) ³ = (x-y²) (x²+xy² + (y²) ²) = (x-y²) (x²+xy²+y⁴).