Add $(a + 1) (a^{2} - a + 1) a n d (a - 1) (a^{2} + a + 1);$

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Solution

$(a + 1) (a^{2} - a + 1) + (a - 1) (a^{2} + a + 1)$
$= a^{3} - a^{2} + a + a^{2} - a + 1 + a^{3} + a^{2} + a - a^{2} - a - 1$
$= 2 a^{3}$

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