Factorize $5 x^{2} - 9 y^{2}$ for $x = 2, y = 1$

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Solution

$5 x^{2} - 9 y^{2} = (\sqrt{5} x)^{2} - (3 y)^{2}$
$\Rightarrow (\sqrt{5} x + 3 y) (\sqrt{5} x - 3 y) ∴$ for $x = 2, y = 1$
$\Rightarrow (3 + 2 \sqrt{5}) (2 \sqrt{5} - 3) = 11$

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9 x^{2} - 16 y^{2}

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