Trig simplification (this one is tough)

f(x)= (4cos (x) -cos (3x))^2 + (3sin (x) -sin (3x))^2

f(x) has to be simplified to the form: f(x)= a cos ^2 (2x) + b cos (2x) + c where a,b,and c are real numbers.

so far I expanded the two parentheticals to: f(x)= 16 cos ^2 (x) - 8 cos(x) cos(3x) + cos ^2 (3x) + 9 sin^2 (x) -6 sin (x) sin (3x) + sin ^2 (3x)

after this I'm stumped.

I tried merging the 16cos ^2 (x) + sin ^2 (3x) to a 7 cos ^2(x) + 9, and doing the same with the sin ^2 (3x) + cos ^2 (3x) = 1. But it isn't taking me anywhere.

If someone can solve this with work, I would highly appreciate it!

Thanks

-kaplac