Factorise : $16 - a^{4}$

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Solution

$16 - a^{4} = 4^{2} - (a^{2})^{2}$
Now use the inentity $a^{2} - b^{2} = (a + b) (a - b)$
$4^{2} - (a^{2})^{2} = (4 + a^{2}) (4 - a^{2})$
$= (4 + a^{2}) (2 + a) (2 - a)$
$S o, 16 - a^{4} = (4 + a^{2}) (2 + a) (2 - a)$

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