Factorize each of the following expressions:$(x + 2)^3 + (x- 2)^3$

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,

$(x + 2)^3 + (x - 2)^3 = (x + 2 + x - 2) [(x + 2)^2 - (x + 2) (x - 2) + (x - 2)^2]$

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

$= 2x[x^2 + 4x + 4 - x^2 + 4+ x^2 - 4x + 4]$

$= 2x[x^2 + 12]$

Hence, $(x + 2)^3 + (x - 2)^3 = 2x[x^2 + 12]$.

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Updated on: 10-Oct-2022

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