Question

(lg2)^3+3lg5(lg2)^2+3lg2(lg5)^2+(lg5)^3~~下一步怎么化简？？？

(lg2)^3+3lg5(lg2)^2+3lg2(lg5)^2+(lg5)^3
下一步怎么化简？？？~~~~~
求公式或者理由……

Answer 1

lg2+lg5=lg2*5=lg10=1
后面反复用到这个

(lg2)^3+3lg5(lg2)^2+3lg2(lg5)^2+(lg5)^3
=[(lg2)^3+(lg5)^3]+3lg5(lg2)^2+3lg2(lg5)^2
=(lg2+lg5)[(lg2)^2-lg2lg5+(lg5)^2]+3lg2lg5(lg2+lg5)
=(lg2)^2-lg2lg5+(lg5)^2+3lg2lg5
=(lg2)^2+2lg2lg5+(lg5)^2
=(lg2+lg5)^2
=1

Answer 2

(a+b)^3=a^3+3ba^2+3ab^2+b^3