Problem: ((x3+1)2(x+1)2(x2−x+1)2)2⋅[(x3−1)2(x−1)2(x2+x+1)2]2 equals:
Answer Choices:
A. (x+1)4
B. (x3+1)4
C. 1
D. [(x3+1)(x3−1)]2
E. [(x3−1)2]2
Solution:
Since x3+1=(x+1)(x2−x+1) and
x3−1=(x−1)(x2+x+1)
the given expression, when simplified, is 1 (with suitable restrictions on the value of x ).