Question

（lg2)2[2lg5+1]+(lg5)2[2lg2+lg10]

Answer 1

(lg2)^2*(2lg5+lg10)+(lg5)^2*(2lg2+lg10)

=(lg2)^2*(2lg5+1)+(lg5)^2*(2lg2+1)

=2(lg2)^2lg5+(lg2)^2+2(lg5)^2lg2+(lg5)^2

=2lg2lg5(lg2+lg5)+(lg2)^2+(lg5)^2

=2lg2lg5+(lg2)^2+(lg5)^2

=(lg2+lg5)^2

=1