Solution
$$x^4 + 64 = (x^2 + 8)^2 - (4x)^2$$
=$$((x^2 + 8) - 4x)((x^2 +8) +4x)$$
=$$(x^{2}+4x+8)(x^{2}-4x+8)$$
So, the answer would be option d)$$(x^{2}+4x+8)(x^{2}-4x+8)$$
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