(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