Question

lg5^2+2/3lg8+lg5*lg20+（lg2）^2=?

Answer 1

lg5^2+2/3lg8+lg5*lg20+（lg2）^2

=2lg5+2/3lg2^3+lg5*lg5*2^2 +（lg2）^2

=2lg5+2/3 * 3 lg2+lg5(lg5+2lg2)+（lg2）^2

=2lg5+2lg2+(lg5)^2+2lg5lg2+(lg2)^2

=2(lg5+lg2)+(lg5)^2+2lg5lg2+(lg2)^2

=2lg10 + (lg5+lg2)^2

=2+(lg10)^2

=2+1=3