Factorize each of the following expressions:$p^3 + 27$

Given:

$p^3 + 27$

To do:

We have to factorize the given expression.

Solution:

We know that,

$a^3 + b^3 = (a + b) (a^2 - ab + b^2)$

$a^3 - b^3 = (a - b) (a^2 + ab + b^2)$
Therefore,
$p^3 + 27 = (p)^3 + (3)^3$

$= (p + 3) (p^2 - p \times 3 + 3^2)$

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

Hence, $p^3 + 27 = (p + 3) (p^2 - 3p + 9)$.

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Updated on: 10-Oct-2022

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