因式分解.(a²-1)(b²-1)+4ab

问题描述:

因式分解.(a²-1)(b²-1)+4ab

(a²-1)(b²-1)+4ab=a²b²-a²-b²+1+4ab
=-[(a-b)²-2ab]+(a²b²+1)
=-(a-b)²+(ab+1)²
=(ab+1)²-(a-b)²
=(ab+a-b+1)(ab-a+b+1)

=a²b²-a²-b²+1+4ab