Simplify $(2a + 5)(2a - 5) - (a + 1)(a - 1)$.

Simplify $(2a + 5)(2a - 5) - (a + 1)(a - 1)$.
  1. $3a^{2} - 24$
  2. $3a^{2} + 24$
  3. $5a^{2} - 24$
  4. $3a^{2} - 26$

Solution

$(4a^{2} - 25) - (a^{2} - 1) = 4a^{2} - 25 - a^{2} + 1 = 3a^{2} - 24$.

Asked in: IMO

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