Multiply $(2x^{2} - 3y^{2})$ by $(x^{2} + y^{2})$.

Multiply $(2x^{2} - 3y^{2})$ by $(x^{2} + y^{2})$.
  1. $2x^{4} - x^{2}y^{2} - 3y^{4}$
  2. $2x^{4} + x^{2}y^{2} - 3y^{4}$
  3. $2x^{4} - x^{2}y^{2} + 3y^{4}$
  4. $2x^{4} - 5x^{2}y^{2} - 3y^{4}$

Solution

$2x^{2} \cdot x^{2} + 2x^{2}\cdot y^{2} - 3y^{2}\cdot x^{2} - 3y^{2}\cdot y^{2} = 2x^{4} + 2x^{2}y^{2} - 3x^{2}y^{2} - 3y^{4} = 2x^{4} - x^{2}y^{2} - 3y^{4}$.

Asked in: IMO

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