Subtract the sum of $(2x - 3y + z)$ and $(x + 2y - 3z)$ from $(5x + y - 2z)$.

Subtract the sum of $(2x - 3y + z)$ and $(x + 2y - 3z)$ from $(5x + y - 2z)$.
  1. $2x + 2y$
  2. $8x - 4z$
  3. $2x - 2y + 4z$
  4. $2x + 2y - 4z$

Solution

Sum of first two = $3x - y - 2z$. Subtract from $5x + y - 2z$: $(5x - 3x) + (y-(-y)) + (-2z - (-2z)) = 2x + 2y + 0 = 2x + 2y$.

Asked in: IMO

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