A function f is even if: f(-x) = f(x)

A function f is off if: f(-x) = -f(x)

a) Suppose that f and g are both odd. Prove that y = f(x)g(x) is even.

b) suppose that f is even and g is odd. Prove that y = f(x)g(x) is odd.

c) Suppose that f and g are botheven. Prove that y = f(x)g(x) is odd.

My attempt for a), but I'm not sure if I did it correctly.

f(-x)g(-x) = -f(x) (-g(x))

Then I brought the (-)'s out on the left side

-f(x) (-g(x))= -f(x) (-g(x))

How would I do b and c) if it's not correct?