(a) Prove that if a, b, c, d, e, f are nonnegative real numbers, then (a^2 + b^2)^2 (c^4 + d^4)(e^4 + f^4) >= 16 a^2 b^2 c^2 d^2 e^2 f^2.

(b) Prove that if a, b, c, d, e, f are nonnegative real numbers, then (a^2 + b^2)(c^2 + d^2)(e^2 + f^2) >= 8 abcdef.