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

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Solution

We need to factorise $49 x^{2} - 25 y^{2}$
The given expression can be factorised by using property $(a^{2} - b^{2}) = (a + b) (a - b)$
It can be written as $49 x^{2} - 25 y^{2} = (7 x)^{2} - (5 y)^{2}$
Here $a = 7 x, b = 5 y$
Hence, $(49 x^{2} - 25 y^{2}) = (7 x + 5 y) (7 x - 5 y)$

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