Factorise:
(i) $a^{4} - b^{4}$
(ii) $p^{4} - 81$

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Solution

(i)To factorise: $a^{4} - b^{4}$
Now,
$a^{4} - b^{4}$
$= (a^{2})^{2} - (b^{2})^{2}$
$= (a^{2} - b^{2}) (a^{2} + b^{2})$
$= (a - b) (a + b) (a^{2} + b^{2})$
(ii) To factorise: $p^{4} - 81$

Now,
$p^{4} - 81$
$= (p^{2})^{2} - (9)^{2}$
$= (p^{2} - 9) (p^{2} + 9)$
$= (p^{2} - 3^{2}) (p^{2} + 9)$
$= (p - 3) (p + 3) (p^{2} + 9)$

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