(m-3n)^3-(2m-3n)(3mn+(m-3n)^2)=-m^3 докажите справедливость равенства

Question

(m-3n)^3-(2m-3n)(3mn+(m-3n)^2)=-m^3 докажите справедливость равенства

Answer 1

1) (m-3n)³= m3-9m²n+27mn²-27n³
2) (m-3n)²= m²-6mn+9n²
3) 3mn+m²-6mn+9n²=m²-3mn+n²
4) (2m-3n)(m²-3mn+n²) = 2m³-6m²n+2mn²-3m²n+9mn²-3n³ = 2m³-9m²n--mn²-3n³
5) m³-9m²n+27mn²-27n³-2m³+9m²n+mn²+3n³ = -m³+28mn²-24n³