A complete factorisation of (x4 + 64) is

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1. (x² + 8)²
2. (x² + 8)(x² − 8)
3. (x² − 4x + 8) (x² – 4x – 8)
4. (x² + 4x + 8) (x² – 4x + 8)

x⁴ + 64 = (x²)² + (8)²
= (x² + 8)² – 2 × 8x²
[∵ a² + b² = (a + b)² – 2ab]
= (x² + 8)² – (4x)²
= (x² + 4x + 8) (x² – 4x + 8)