Factorise: $5 x^{2} - 7 y^{2}$

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Solution

Since we know the identity $a^{2} - b^{2} = (a + b) (a - b)$

Using the above identity, the equation $5 x^{2} - 7 y^{2}$ can be factorised as follows:

$5 x^{2} - 7 y^{2}$
$= (\sqrt{5} x)^{2} - (\sqrt{7} y)^{2}$
$= (\sqrt{5} x + \sqrt{7} y) (\sqrt{5} x - \sqrt{7} y)$

Hence, $5 x^{2} - 7 y^{2} = (\sqrt{5} x + \sqrt{7} y) (\sqrt{5} x - \sqrt{7} y)$

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