(lg2)³+(lg5)³+3lg2×lg5=?请问这道数学题怎么做?

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(lg2)³+(lg5)³+3lg2×lg5=?请问这道数学题怎么做?
(lg2)³+(lg5)³+3lg2×lg5=?请问这道数学题怎么做?

(lg2)³+(lg5)³+3lg2×lg5=?请问这道数学题怎么做?
(lg2)³+(lg5)³+3lg2×lg5
=(lg2+lg5)(lg²2+lg²5-lg2lg5)+3lg2×lg5
=lg²2+lg²5-lg2lg5+3lg2lg5
=(lg2+lg5)²
=1