Question

Помогите упростить выражения:1)x^38-x^2y4+xy^26-y^327
2)125m327+125m^2n6+125mn^24+125n^38

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.