Factorize :
$(x + 1)^{3} + (x - 1)^{3}$

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Solution

$(x + 1)^{3} + (x - 1)^{3}$
$= [(x + 1) + (x - 1)] [(x + 1)^{2} - (x + 1) (x - 1) + (x - 1)^{2}]$
$= (x + 1 + x - 1) [(x^{2} + 2 x + 1) - (x^{2} - 1) + (x^{2} - 2 x + 1)]$
$= 2 x (x^{2} + 2 x + 1 - x^{2} + 1 + x^{2} - 2 x + 1)$
$= 2 x (x^{2} + 3)$

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