Factorise $a^{2} - (b - c)^{2}$.

Factorise $a^{2} - (b - c)^{2}$.
  1. $(a - b + c)(a + b - c)$
  2. $(a + b + c)(a - b + c)$
  3. $(a - b - c)(a + b + c)$
  4. $(a + b - c)(a + b + c)$

Solution

$a^{2} - (b-c)^{2} = [a-(b-c)][a+(b-c)] = (a-b+c)(a+b-c)$.

Asked in: IMO

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