(lg5)^2 +2(lg)^2 +1-(lg2)^2

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(lg5)^2+2(lg)^2+1-(lg2)^2(lg5)^2+2(lg)^2+1-(lg2)^2(lg5)^2+2(lg)^2+1-(lg2)^2=lg²5-lg²2+2lg2

(lg5)^2 +2(lg)^2 +1-(lg2)^2
(lg5)^2 +2(lg)^2 +1-(lg2)^2

(lg5)^2 +2(lg)^2 +1-(lg2)^2
=lg²5-lg²2+2lg2
=(lg5+lg2)×(lg5-lg2)+2lg2
=lg5-lg2+2lg2
=lg5+lg2
=1