lg2×lg2500+2(lg5)^2
=lg2×2lg50+2(lg5)^2
=2lg2×(lg2+lg25)+2(lg5)^2
=2(lg2)^2+2lg2lg25+2(lg5)^2
=2(lg2)^2+4lg2lg5+2(lg5)^2
=2[lg2+lg5]^2
=2(lg10)^2
=2*1^2
=2