Answer
$x^4-16$
Work Step by Step
The product of a binomial sum and a binomial difference is: $(A+B)(A-B)=A^2-B^2$.
The square of a binomial sum is: $(A+B)^2=A^2+2AB+B^2$.
The square of a binomial difference is: $(A-B)^2=A^2-2AB+B^2$.
Hence here: $(x+2)(x-2)(x^2+4)=(x^2-2^2)(x^2+4)=(x^2-4)(x^2+4)=(x^2)^2-4^2=x^4-16$