Factorise $p^4 -81$.

Given:

$p^4 -81$.

To do:

We have to factorise $p^4 -81$.
Solution:

We know that,

$a^2-b^2=(a+b)(a-b)$

Therefore,

$p^4 -81=(p^2)^2-(9)^2$ 

$=(p^2-9)(p^2+9)$

$=[(p)^2-(3)^2](p^2+9)$

$=(p-3)(p+3)(p^2+9)$.

Therefore, $p^4-81=(p-3)(p+3)(p^2+9)$.

Tutorialspoint

Updated on: 10-Oct-2022

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