HOW TO SIMPLY (log a/b)^2 + 4logalogb - (logab)^2

(log a/b)^2 + 4logalogb - (logab)^2
= (log a-logb)^2 + 4logalogb - (loga+logb)^2
= (log a)^2 - 2logalogb +(log b)^2 +4logalogb - ((log a)^2 + 2logalogb +(log b)^2)
= (log a)^2 - 2logalogb +(log b)^2 +4logalogb - (log a)^2 - 2logalogb -(log b)^2
= 0

(log a/b)^2 + 4logalogb - (logab)^2
=(log a-log b)^2-(log a+log b)^2+4log a log b
=(2log a)(-2log b)+4log a log b<-----------a^2-b^2=(a+b)(a-b)
=-4log a log b+4log a log b
=0

Here is the solution:

圖片參考：http://xs413.xs.to/xs413/07105/ggdgdgrgrg.png

(log a/b)^2 + 4logalogb - (logab)^2
= (log a - log b)^2 + 4 logalogb - (log a + log b)^2
>>>log a/b = log a - log b and logab = log a + log b

= (log a)^2 - 2logalogb + (log b)^2 + 4 logalogb - (log a)^2 - 2 logalogb - (log b)^2
>>>乘開 (log a - log b)^2 同埋 (log a + log b)^2

= 0