Cauchy-Schwarz Inequality Question

Let a, b, c, d, e, f be nonnegative real numbers.

 

(a) Prove that 

\((a^2 + b^2)^2 (c^4 + d^4)(e^4 + f^4) \ge (ace + bdf)^4.\)

 

(b) Prove that

\((a^2 + b^2)(c^2 + d^2)(e^2 + f^2) \ge (ace + bdf)^2.\)