Factorise the following
$81 x^{4} - 121 x^{2}$

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Solution

$81 x^{4} - 121 x^{2} = x^{2} (81 x^{2} - 121) = x^{2} ((9 x)^{2} - (11)^{2}) = x^{2} (9 x + 11) (9 x - 11)$

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81 x^{4} - 121 x^{2}

81 x^{4} - 121 x^{2}

81 x^{4} - 16 y^{4}

3 x - \frac{1}{3 x} = 15

81 x^{4} + \frac{1}{81 x^{4}}

If $3 x - \frac{1}{3 x} = 5$ , find :

(i) $9 x^{2} + \frac{1}{9 x^{2}}$

(ii) $81 x^{4} + \frac{1}{81 x^{4}}$

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