Factorise $9(x+y)^{2} - 4(x-y)^{2}$.

Factorise $9(x+y)^{2} - 4(x-y)^{2}$.
  1. $(x + 5y)(5x + y)$
  2. $(5x - y)(x + 5y)$
  3. $(5x + y)(x - 5y)$
  4. $(3x + 3y - 2x + 2y)^{2}$

Solution

Rewrite as $[3(x+y)]^{2} - [2(x-y)]^{2} = [3(x+y)-2(x-y)][3(x+y)+2(x-y)] = (x + 5y)(5x + y)$.

Asked in: IMO

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