Find the product $3xy^{2} \cdot (2x^{2} - 5xy + y^{2})$.

Find the product $3xy^{2} \cdot (2x^{2} - 5xy + y^{2})$.
  1. $6x^{3}y^{2} - 15x^{2}y^{3} + 3xy^{4}$
  2. $6x^{3}y^{2} - 15x^{2}y^{3} - 3xy^{4}$
  3. $6x^{3}y^{2} + 15x^{2}y^{3} + 3xy^{4}$
  4. $6x^{2}y^{3} - 15x^{3}y^{2} + 3xy^{4}$

Solution

$3xy^{2} \cdot 2x^{2} = 6x^{3}y^{2}$; $3xy^{2}\cdot(-5xy) = -15x^{2}y^{3}$; $3xy^{2}\cdot y^{2} = 3xy^{4}$.

Asked in: IMO

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