Factorize each of the following expressions:$1 - 27a^3$

Given:

$1 - 27a^3$

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,

$1 - 27a^3 = (1)^3 - (3a)^3$

$= (1 - 3a) [1^2 + 1 \times 3a + (3a)^2]$

$= (1 - 3a) (1 + 3a + 9a^2)$

Hence, $1 - 27a^3 = (1 - 3a) (1 + 3a + 9a^2)$.

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Updated on: 10-Oct-2022

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