lg²2 + lg50 + lg2*lg5
= lg²2+ lg2*lg5 + lg50
= lg2 * ( lg2+ lg5) + lg50
= lg2 * lg(2*5) + lg50
= lg2 * lg10 + lg50
= lg2 + lg50
= lg(2*50)
= lg100
= lg10²
= 2