Factorise: $x^{4} - 16$.

Factorise: $x^{4} - 16$.
  1. $(x - 2)(x + 2)(x^{2} + 4)$
  2. $(x^{2} - 4)^{2}$
  3. $(x - 2)^{2}(x + 2)^{2}$
  4. $(x^{2} + 4)^{2}$

Solution

$x^{4} - 16 = (x^{2})^{2} - 4^{2} = (x^{2}-4)(x^{2}+4)$. Further $x^{2}-4 = (x-2)(x+2)$.

Asked in: IMO

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