Find the factor of $16 a^{4} - 81 b^{4}$

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Solution

${16 a}^{4} - 81 b^{4} \Rightarrow {(4 a^{2})}^{2} - {(9 b^{2})}^{2}$
$\Rightarrow ({4 a}^{2} - {9 b}^{2}) ({4 a}^{2} + {9 b}^{2})$
$\Rightarrow [{(2 a)}^{2} - {(3 b)}^{2}] ({4 a}^{2} + {9 b}^{2})$
$\Rightarrow (2 a - 3 b) (2 a + 3 b) ({4 a}^{2} + {9 b}^{2})$

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