a^(n+2)-8a^n+16a^(n-2)
=a^4*a^(n-2)-8*a^2*a^(n-2)+16a^(n-2)
=(a^4-8a^2+16)*a^(n-2)
=a^(n-2)(a^2-4)^2
=a^(n-2)[(a-2)(a+2)]^2
=a^(n-2)(a-2)^2(a+2)^2