Problem: The factors of the expression x2+y2x^{2}+y^{2}x2+y2 are
Answer Choices:
A. (x+y)(x−y)(x+y)(x-y)(x+y)(x−y)
B. (x+y)2(x+y)^{2}(x+y)2
C. (x2/3+y2/3)(x4/3+y4/3)\left(x^{2 / 3}+y^{2 / 3}\right)\left(x^{4 / 3}+y^{4 / 3}\right)(x2/3+y2/3)(x4/3+y4/3)
D. (x+iy)(x−iy)(x+iy)(x-iy)(x+iy)(x−iy)
E. none of these Solution:
x2+y2x^{2}+y^{2}x2+y2 has no linear factors in the real field. x2+y2=(x+iy)(x−iy)x^{2}+y^{2}=(x+i y)(x-i y)x2+y2=(x+iy)(x−iy) in the complex field.