Factorise: $49x^{2} - 25y^{2}$.

Factorise: $49x^{2} - 25y^{2}$.
  1. $(7x - 5y)(7x + 5y)$
  2. $(7x - 5y)^{2}$
  3. $(49x - 25y)(x + y)$
  4. $(7x + 5y)^{2}$

Solution

$49x^{2} = (7x)^{2}$ and $25y^{2} = (5y)^{2}$. Apply $a^{2} - b^{2} = (a-b)(a+b)$.

Asked in: IMO

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