What should be subtracted from $4y^{2} - 3y + 8$ to get $y^{2} + 2y - 5$?

What should be subtracted from $4y^{2} - 3y + 8$ to get $y^{2} + 2y - 5$?
  1. $3y^{2} - 5y + 13$
  2. $3y^{2} + 5y - 13$
  3. $5y^{2} - y + 3$
  4. $3y^{2} - 5y - 13$

Solution

Required = $(4y^{2} - 3y + 8) - (y^{2} + 2y - 5) = 3y^{2} - 5y + 13$.

Asked in: IMO

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