Problem: The fraction a2+c2−b2+2aca2+b2−c2+2ab​ is (with suitable restrictions on the values of a,b, and c):
Answer Choices:
A. irreducible
B. reducible to -1
C. reducible to a polynomial of three terms
D. reducible to a+b−ca−b+c​
E. reducible to a−b+ca+b−c​
Solution:
a2+c2−b2+2aca2+b2−c2+2ab​=(a+c)2−b2(a+b)2−c2​=(a+c+b)(a+c−b)(a+b+c)(a+b−c)​
=a+c−ba+b−c​ with (a+c)2î€ =b2