(1) First: lg2+lg5= 1.

Then (lg5) 2+2 * lg2 * (lg2+lg5)-(lg2) 2

=(lg5+lg2)^2

= 1

(2) First, lg50=lg2+2lg5.

lg25=2lg5

The above formula = (lg2) 2+lg2 * (lg2+2 * lg5)+2lg5.

=2[(lg2)^2+lg2*lg5+lg5]

=2[(lg2)^2+lg2*lg5+lg5*(lg2+lg5)]

=2(lg2+lg5)^2

=2