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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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