The first step for this problem is to map out what the probability that x is even:
$ P{X is Even}= ∑_█(k=0@k even)^N▒P[x=k] = ∑_█(k=0@k even)^n▒〖(n¦k) x^k a^(n-k) 〗 $
Next we must expand $ (x+y)^n 〖+ (x-y)〗^n $ using the binomial thereom:
$ (x+y)^n 〖+ (x-y)〗^n=∑_(k=0)^n▒〖(n¦k) y^k x^(n-k) + ∑_(k=0)^n▒〖(n¦k) 〖(-y)〗^k x^(n-k) 〗〗 $
