Subtract $-3a^{2} + 5ab - 2b^{2}$ from $a^{2} - ab + b^{2}$.

Subtract $-3a^{2} + 5ab - 2b^{2}$ from $a^{2} - ab + b^{2}$.
  1. $4a^{2} - 6ab + 3b^{2}$
  2. $4a^{2} + 4ab + 3b^{2}$
  3. $-2a^{2} - 6ab + 3b^{2}$
  4. $4a^{2} - 6ab - b^{2}$

Solution

$(a^{2} - ab + b^{2}) - (-3a^{2} + 5ab - 2b^{2}) = a^{2}+3a^{2} - ab - 5ab + b^{2} + 2b^{2} = 4a^{2} - 6ab + 3b^{2}$.

Asked in: IMO

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