Simplify $5(x^{2} - 2xy) - 3(x^{2} + xy - y^{2}) + 2(xy + y^{2})$.

Simplify $5(x^{2} - 2xy) - 3(x^{2} + xy - y^{2}) + 2(xy + y^{2})$.
  1. $2x^{2} - 11xy + 5y^{2}$
  2. $2x^{2} + 11xy + 5y^{2}$
  3. $8x^{2} - 11xy + 5y^{2}$
  4. $2x^{2} - 11xy - 5y^{2}$

Solution

$= 5x^{2} - 10xy - 3x^{2} - 3xy + 3y^{2} + 2xy + 2y^{2} = (5-3)x^{2} + (-10-3+2)xy + (3+2)y^{2} = 2x^{2} - 11xy + 5y^{2}$.

Asked in: IMO

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