Problem: An equivalent of the expression (xx2+1β)(yy2+1β)+(yx2β1β)(xy2β1β),xyξ =0, is:
Answer Choices:
A. 1
B. 2xy
C. 2x2y2+2
D. 2xy+xy2β
E. y2xβ+x2yβ
Solution:
The given expression equals (x+x1β)(y+y1β)+(xβx1β)(yβy1β)
=xy+xyβ+yxβ+xy1β+xyβxyββyxβ+xy1β=2xy+xy2β.
or
The given expression equals xyx2y2+x2+y2+1+x2y2βx2βy2+1β=xy2x2y2+2β=2xy+xy2β.