Factorise $x^{4} - y^{4}$.

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

Solution

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

Asked in: IMO

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