Question

Помогите упростить выражения:1)x^3\8-x^2y\4+xy^2\6-y^3\27
2)125m3\27+125m^2n\6+125mn^2\4+125n^3\8

Answer 1

1) x³/8-x²y/4+xy²/6-y³/27=(x/2)³-x²y/4+xy²/6-(y/3)³=(x/2-y/3)³.
3*(x/2)²*(y/3)=3*(x²/4)*(y/3)=x²y/4        3*(x/2)*(y/3)²=3*(x/2)*(y²/9)=xy²/6   ⇒
2) 125m/27+125m²n/6+125mn²/4+125n³/8=
=(5m/3)³+3*(5m/3)²*(5n/2)+3*(5m/3)*(5n/2)²+(5n/2)³=(5m/3+5n/2)³.