Question:
\[ (x-y)(x+y)(x^2+y^2)(x^4+y^4) \] is equal to
(a) \[ x^{16}-y^{16} \]
(b) \[ x^8-y^8 \]
(c) \[ x^8+y^8 \]
(d) \[ x^{16}+y^{16} \]
Solution:
Using identity:
\[ (x-y)(x+y)=x^2-y^2 \]
Therefore,
\[ (x^2-y^2)(x^2+y^2) = x^4-y^4 \]
Now,
\[ (x^4-y^4)(x^4+y^4) = x^8-y^8 \]
Hence,
\[ (x-y)(x+y)(x^2+y^2)(x^4+y^4) = x^8-y^8 \]
Therefore, the correct answer is:
\[ \boxed{x^8-y^8} \]