Factorize the following expression:

$16 a^{4} - b^{4}$

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Solution

Given: $16 a^{4} - b^{4}$

$∴ 16 a^{4} - b^{4}$
$= (4 a^{2})^{2} - (b^{2})^{2}$
Using the formula, $(x^{2} - y^{2}) = (x - y) (x + y)$
$= (4 a^{2} + b^{2}) (4 a^{2} - b^{2})$
$= (4 a^{2} + b^{2}) [(2 a)^{2} - b^{2}]$
$= (4 a^{2} + b^{2}) (2 a + b) (2 a - b)$

Hence, $16 a^{4} - b^{4} = (4 a^{2} + b^{2}) (2 a + b) (2 a - b)$

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If $2 a + \frac{1}{2 a} = 8$ , find :

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16 a^{4} - 9 b^{4}

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