Simplify $(x^{2} + 1)(x^{2} - 1)(x^{4} + 1)$.

Simplify $(x^{2} + 1)(x^{2} - 1)(x^{4} + 1)$.
  1. $x^{8} - 1$
  2. $x^{8} + 1$
  3. $x^{6} - 1$
  4. $x^{4} - 1$

Solution

$(x^{2}+1)(x^{2}-1) = x^{4} - 1$. Then $(x^{4}-1)(x^{4}+1) = x^{8} - 1$.

Asked in: IMO

Practice more ALGEBRAIC EXPRESSIONS AND IDENTITIES questions on Aicharya