Factorize each of the following expressions:$8a^3 - b^3 - 4ax + 2bx$

Given:

$8a^3 - b^3 - 4ax + 2bx$

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,

$8a^3 - b^3 - 4ax + 2bx = (2a)^3 - (b)^3 - 2x(2a - b)$

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

$= (2a - b) [4a^2 + 2ab + b^2] - 2x(2a - b)$

$= (2a - b) (4a^2 + 2ab + b^2 - 2x)$

Hence, $8a^3 - b^3 - 4ax + 2bx = (2a - b) (4a^2 + 2ab + b^2 - 2x)$.

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Updated on: 10-Oct-2022

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