(lg2)的平方+(lg5)的立方+3lg2*lg5等于多少?

(lg2)的平方+(lg5)的立方+3lg2*lg5等于多少?
(lg2)的平方+(lg5)的立方+3lg2*lg5等于多少?

(lg2)的平方+(lg5)的立方+3lg2*lg5等于多少?
设x=lg2,y=lg5,则x+y=lg2+lg5=lg2*5=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

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