Answer
$(x+8-x^2)(x+8+x^2)$
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: $x^2+16x+64-x^4=\\=x^2+2\cdot8\cdot x+8^2-(x^2)^2=\\=(x+8)^2-(x^2)^2\\=(x+8-x^2)(x+8+x^2)$