Factorize each of the following expressions:$32a^3 + 108b^3$

Given:

$32a^3 + 108b^3$

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,

$32a^3 + 108b^3 = 4(8a^3 + 27b^3)$

$= 4 [(2a)^3 + (3 b)^3]$

$= 4(2a + 3b) [(2a)^2 - 2a \times 3b + (3b)^2]$

$= 4(2a + 3b) (4a^2 - 6ab + 9b^2)$

Hence, $32a^3 + 108b^3 = 4(2a + 3b) (4a^2 - 6ab + 9b^2)$.

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Updated on: 10-Oct-2022

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