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