Factorize:$a^3 - 3a^2b + 3ab^2 - b^3 + 8$

Given:

$a^3 - 3a^2b + 3ab^2 - b^3 + 8$

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,

$a^3 - 3a^2b + 3ab^2 - b^3 + 8 = (a - b)^3 + (2)^3$

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

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

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

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Updated on: 10-Oct-2022

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