Compute $98 \times 103$ using $(x+a)(x+b)$.

Compute $98 \times 103$ using $(x+a)(x+b)$.
  1. $10094$
  2. $10000$
  3. $10100$
  4. $10084$

Solution

$(100-2)(100+3) = 100^{2} + (1)(100) + (-2)(3) = 10000 + 100 - 6 = 10094$.

Asked in: IMO

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