Factorize each of the following expressions:$a^3 + 8b^3 + 64c^3 - 24abc$

Given:

$a^3 + 8b^3 + 64c^3 - 24abc$

To do:

We have to factorize the given expression.

Solution:

We know that,

$a^3 + b^3 + c^3 - 3abc = (a + b + c) (a^2 + b^2 + c^2 - ab - bc - ca)$

Therefore,

$a^3 + 8b^3 + 64c^3 - 24abc = (a)^3 + (2b)^3 + (4c)^3 - 3 \times a \times 2b \times 4c$

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

$= (a + 2b + 4c) (a^2 + 4b^2 + 16c^2 - 2ab - 8bc - 4ca)$

Hence, $a^3 + 8b^3 + 64c^3 - 24abc = (a + 2b + 4c) (a^2 + 4b^2 + 16c^2 - 2ab - 8bc - 4ca)$.

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Updated on: 10-Oct-2022

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