lg25+lg2*lg50+(lg2)^2+1=?

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lg25+lg2*lg50+(lg2)^2+1=?
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lg25+lg2*lg50+(lg2)^2+1=?
lg25+lg2*lg50+(lg2)^2+1=?

lg25+lg2*lg50+(lg2)^2+1=?
原式=lg5²+lg2*(lg5+lg10)+(lg2)²+1
=2lg5+lg2*lg5+lg2*lg10+(lg2)²+1
=2lg5+lg2+lg2*lg5+(lg2)²+1
=2lg5+lg2+lg2(lg5+lg2)+1
=2lg5+lg2+lg2+1
=2(lg5+lg2)+1
=2+1
=3

=2lg5+(1-lg5)(1+lg5)+(1-lg5)²+1
=2lg5+1-lg²5+1-2lg5+lg²5+1
=3