Factorize each of the following expressions:$(a + b)^3 - 8(a - b)^3$

Given:

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,

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

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

$= (3b - a) [a^2 + b^2 + 2ab + 2a^2 - 2ab + 2ab - 2b^2 + 4a^2 - 8ab + 4b^2]$

$= (3b - a) [7a^2 - 6ab + 3b^2]$

Hence, $(a + b)^3 - 8(a - b)^3 = (3b - a) [7a^2 - 6ab + 3b^2]$.

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Updated on: 10-Oct-2022

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