Factorise $1 + 4x + 4x^{2}$.

Factorise $1 + 4x + 4x^{2}$.
  1. $(1 + 2x)^{2}$
  2. $(1 - 2x)^{2}$
  3. $(1 + 2x)(1 - 2x)$
  4. $(1 + 4x)(1 + x)$

Solution

$1+4x+4x^{2} = 1^{2} + 2 \cdot 1 \cdot 2x + (2x)^{2} = (1+2x)^{2}$.

Asked in: IMO

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