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

Multiply: $(x + 2y)(x - 2y)(x^{2} + 4y^{2})$.
  1. $x^{4} - 16y^{4}$
  2. $x^{4} + 16y^{4}$
  3. $x^{4} - 8y^{4}$
  4. $x^{4} - 4y^{4}$

Solution

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

Asked in: IMO

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