Problem: An equivalent of the expression (xx2+1​)(yy2+1​)+(yx2−1​)(xy2−1​),xyî€ =0, is:
Answer Choices:
A. 1
B. 2xy
C. 2x2y2+2
D. 2xy+xy2​
E. y2x​+x2y​
Solution:
The given expression equals (x+x1​)(y+y1​)+(x−x1​)(y−y1​)
=xy+xy​+yx​+xy1​+xy−xy​−yx​+xy1​=2xy+xy2​.
or
The given expression equals xyx2y2+x2+y2+1+x2y2−x2−y2+1​=xy2x2y2+2​=2xy+xy2​.