A complete factorisation of x⁴ + 64 is?

A. (x² + 8)²

B. (x² + 8)(x² - 8)

C. (x² - 4x + 8)(x² - 4x - 8)

D. (x² + 4x + 8)(x² - 4x + 8)

Answer: Option D

Solution(By Examveda Team)

$$\eqalign{ & \left( {{x^4} + 64} \right) \cr & = {x^4} + {8^2} + 2.{x^2}.8 - 2.{x^2}.8 \cr & = {\left( {{x^2} + 8} \right)^2} - \left( {16{x^2}} \right) \cr & = {\left( {{x^2} + 8} \right)^2} - {\left( {4x} \right)^2} \cr & = \left( {{x^2} + 8 + 4x} \right)\left( {{x^2} + 8 - 4x} \right) \cr & = \left( {{x^2} + 4x + 8} \right)\left( {{x^2} - 4x + 8} \right) \cr} $$