The given expression is
x^4 - 16
This can be written as
x^4 - 4^2
(x^2)^2 - 4^2
According to the difference of two squares rule, A^2 - B^2 = (A + B)(A - B)
By applying this rule, it becomes
(x^2 - 4)(x^2 + 4)
We would simplify x^2 - 4
x^2 - 4 = x^2 - 2^2
Applying the difference of two squares rule, it becomes
(x - 2)(x + 2)
We would simplify x^2 + 4 = x^2 + 2^2
This would not give us real factors. Hence, it would result in complex numbers
A^2 + B^2 = A^2 - (- 1*B^2) = A^2 - (iB)^2 = (A + iB)(A - iB)
By applying this rule, it becomes
x^2 + 2^2 = (x + 2i)(x - 2i)
Therefore, the complete factorisation would be
(x - 2)(x + 2) (x + 2i)(x - 2i)