1.[x(x^2y^2-xy)-y(x^2-x^3y)]÷3x^2y
=[x^3y^2-x^2y-x^2y+x^3y^2]÷3x^2y
=(2x^3y^2-2x^2y)÷3x^2y
=2xy/3 - 2/3
2.a^2-1+b^2-2ab
=a^2-2ab+b^2-1
=(a-b)^2-1
=(a-b+1)(a-b-1)
3.由已知
两式相减：m^2-n^2=n+2-(m+2) 即m+n=-1
两式相加：m^2+n^2=n+2+m+2 即 m^2+n^2=3
由1,2可以推出 mn=-1
m^3-2mn+n^3=(m+n)(m^2-mn+n^2)-2mn
=(-1)[3-(-1)]-2(-1)
=-2