A complete factorisation of x4 + 64 is?

Answer: Option D

$$\begin{array}{rl}& \left(x^4+64\right)\\ & =x^4+8^2+2.x^2.8-2.x^2.8\\ & ={\left(x^2+8\right)}^2-\left(16x^2\right)\\ & ={\left(x^2+8\right)}^2-{\left(4x\right)}^2\\ & =\left(x^2+8+4x\right)\left(x^2+8-4x\right)\\ & =\left(x^2+4x+8\right)\left(x^2-4x+8\right)\end{array}$$