Question

(lg2)^3+(lg5)^3+3lg5*lg2怎么算谢谢！

Answer 1

a³+b³=(a+b)(a²-ab+b²)

(lg2)^3+(lg5)^3+3lg5*lg2
=(lg2+lg5)[(lg2)²-lg2*lg5+(lg5)²]+3lg2*lg5
=(lg10)[(lg2)²-lg2*lg5+(lg5)²]+3lg2*lg5
=(lg2)²-lg2*lg5+(lg5)²+3lg2*lg5
=(lg2)²+2lg2*lg5+(lg5)²
=(lg2+lg5)²
=(lg10)²
=1²
=1

Answer 2

(lg2)^3+(lg5)^3+3lg5*lg2
=(lg2+lg5)[(lg2)^2-lg2lg5+(lg5)^2)+lg5lg2
=1×[(lg2)^2-lg2lg5+(lg5)^2)+lg5lg2
=(lg2)^2+2lg2lg5+(lg5)^2
=(lg2+lg5)^2
=1