1.设x=lg2,y=lg5,则x+y=lg2+lg5=lg10=1 原式=x^3+y^3+3xy =(x+y)(x^2-xy+y^2)+3xy =x^2-xy+y^2+3xy =x^2+2xy+y^2 =(x+y)^2 =1 2.lg(x-y)+lg(x+2y)=lg2+lgx+lgy lg(x-y)(x+2y)=lg2xy (x-y)（x+2y)=2xy x^2+xy-2y^2=2x...