Expand $(2x - 3)(x^{2} + x - 4)$.

Expand $(2x - 3)(x^{2} + x - 4)$.
  1. $2x^{3} - x^{2} - 11x + 12$
  2. $2x^{3} + x^{2} - 11x + 12$
  3. $2x^{3} - x^{2} + 11x + 12$
  4. $2x^{3} - x^{2} - 11x - 12$

Solution

$2x \cdot (x^{2}+x-4) = 2x^{3} + 2x^{2} - 8x$. $-3(x^{2}+x-4) = -3x^{2} - 3x + 12$. Sum = $2x^{3} - x^{2} - 11x + 12$.

Asked in: IMO

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